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THIS DOCUMENT CONTAINS INFORMATION AFFECTING THE NATIONAL DEFENSE OF THE UNITED STATES WITHIN THE MEANING OF THE ESPIONAGE LAWS, TITLE 18, U.S.C., SECTIONS 793 AND 794. THE TRANSMISSION OR THE REVELATION OF ans CONTENTS IN ANY MANNER TO AN UNAUTHORIZED PERSON IS PROHIBITED BY Si Soc ne Ue Se. NOTICE: When government or other drawirgs, specifications or other data are used for any purpose other than in connection with a defi- nitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data is not to be regarded by implication or otherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use or sell any patented invention that may in any way be related thereto. Sa a Somer = + anilane nage aid te: rotate ‘batial @, bane velvet: 229 eA WO LAS 30, ALY ATM Bek om Pe Meraletiae. ene eon NS 3 bade dumrod ovad y ion meat it JES Bo be pace ole Harty ENTER E BR ARSE MS SERA TCE ae ty SO et kere nes ape eke Be a ATH RESEARCH REPORT REPORT 1049 10 July 1961 = & (ee) as my oO Ke} fe) Kn ct = {o) = Ne) Ade Teche orice ae Oa Gras pase i | _ : C-2 | FORWARDED BY THE CHIE?, DURZAU SS SuIPS of (mn | i; STATISTICAL FILTERS FOR SMOOTHING AND a ne FILTERING EQUALLY SPACED DATA Se as Cy H. M. Linnette fo Ty 4 <2 2G GQ) ie | pi RBe Bol (2 )to Bustin Se i OCT 4 1965 31! 3 tt Lnsres SLi U.S. NAVY ELECTRONICS LABORATORY, SAN DIEGO, CALIFORNIA A BUREAU OF SHIPS LABORATORY (See A A a5 aleve cated oneal THE PROBLEM oe re EY As part of the general study of low frequency amoient sea noise, investigate the characteristies of statistical filters for smoothing of time series data. RESULTS 1. Smoothing with equally weighted running means is computa- tionally simple and resuits in a relatively sharp cutoff filter. However, the frequency response decreases contin- uously within the pass band and high frequency ripples are introduced into the data because of large oscillations in the frequency response above the cutoff. 2. The Gaussian filter does not introduce high frequency ripples into the data since its frequency response approaches zero asymptotically without a finite cutoff. However, its arbitrarily defined 1 per cent cutoff is not very sharp. 3. The defects inherent in the two filters discussed above can be minimized by determining weights for a filter which approximates the square-shaped ideal filter in the least square sense, With corrections for unity gain at zero fre- quency and a sine termination to reduce oscillations above cutoff. Weights have been determined for 118 cuch filters which depart from the ideal filter in the pass-band region and velow the cutoff by an absolute error less than or equa]. to 1 per cent. These weights are given in the Appendix. ADMINISTRATIVE INFORMATION Work was performed under AS 02101, NE 051600-847.60 (now S-ROOK 03 01, Task 8119) (NEL L2-4) from July 1960 through Aprii 1961. This report was approved for publication 10 July 1961. The author wishes to thank G. M. Wenz and E. C. Westerfield for advice and helpful suggestions, and R. F. Arenz for assistance relative to computer programming. aS ae ay : J : a ear rts ee s i Pie Ae cucets % ie, j f = , Z gee: ise eee ai enti us mt ars ied ayew vias bow ‘cee [re Fab: hee Siu peso peer “k tae % Mone or avode re eesge Ss oe sonora) f08 gest! aya ae ett epeRCaEs Se YOREDIT, wit sonia x ad a 7 i eat SOE uy Be ke HORT Pai dente gta Wiis A Rs nisi a he oe en Susi ed Fas wish iia beaw er y ¥ essed Hh etree tig ; : az APSA Pe ere be ae ee rym Seep eo = Page Figure 10 ual 11 2 13 3 14 4 14 5 20 6 21 T 22 8 23 9 25-26 10-11 CONTENTS INTRODUCTION LINEAR FILTERS SMOOTHING OF TIME SERIES FREQUENCY - RESPONSE OF SOME SMOOTHING FUNCTIONS Equally Weighted Running-Mean Smoothing Functions with (241) Consecctive Weights Gaussian Filter FILTERS WHICH APPROXIMATE IDEAL FILTERS WITH UNITY GAIN AND ZERO PHASE SHIFT SUMMARY AND CONCLUSIONS REFERENCES DEFINITIONS APPENDIX: FILTER DATA ILLUSTRATIONS Frequency response of equally weighted running mean weight functions. Variations of cutoff frequency with W for the equally weighted running mean filtering function. Frequency response of the Gaussian weighting function. Variation of the cutoff frequency for the Gaussian filtering function. Frequency response of forty-one term equally weighted running mean compared with an cquivalent normal curve smoothing function. Frequency response function Frequency response versus the normalized frequency Variation of the maximum absolute gain error with h Variation of the maximum absolute gain error with WN Spectral density function versus frequency. = 10 pale eopaien iy, aus din utat on UL Bhi ye ane = ( | Be... oe - WORE Wee ORE Gk Wk i aeM ‘el a: wi Conan re Lc SHOLEAIONOS mee euaoratnaa ae sSNA ¢ epg ional. fore prsieanit ee ee : yes A lees epeieernere't Tigo te sabtyel say rer oe sabe By: wien poet _yoceiniry a say BR emai WSUS sora ch # SS AN Lem Marner TS i a ig eg rt le er Rn RR RNIN) NATRONA A eR ls EP CETERA INTRODUCTION The purpose of this report is to present some of the possibil- ities associated with statistical filtering of periodic data by smoothing and to provide sets of weights to fit some par- ticular cases, for example, the smoothing of low-frequency, ambient sea-noise data. A brief theoretical discussion is included to explain the basic concepts involved. A set of data arranged chronologically is called a time series. Time variations in the data may be relatively smooth or of a complex nature devoid of any apparent pattern. Assuming the Fourier theorem, any variation with time may be considered the result of superposition of a number of simple sinusoidal components, the amplitudes, frequencies, and phases of these components being time-dependent. In many time series it is assumed that high frequency oscilla- tions in the data are either random noise or are of no signif- icance to the particular purpose for which the data are to be evaluated. Consequently, one important purpose of time smoothing is to attenuate the amplitudes of high frequeacy components and, at the same time, preserve the low frequency components of immediate interest. Hence, the smoothed value of an experimentally observed time series is an estimate of its true value free from noise and other undesirable high frequency influences originally present. Smoothing of a time series is a special case of the general process of numerical filtering and is analogous to low-pass filtering of an electrical signal. However, numerical filter- ing includes band-pass and high-pass filtering as weli as low-pass filtering. Thus, if smoothed values are subtracted from the corresponding values in the original unsmoothed time se?.es, only high frequency components will remain. Such an o.ver-tion is equivalent to high-pass filtering. Band-pass filtering may be achicved by subtracting well smoothed values of a time series from corresponding values smoothed to a lesser extent; only intermediate frequencies will remain, thus giving the equivalent of band-pass filter- ing. By use of the above procedures one may separate the oscilla- tions of the time series into particular bands or frequencies, high, intermediate, and low. This report, however, is TT mr Am SRR Ta sR a I ea Ts 3 x # if ke a omen arene tr Utena ne ay Da te Ear 11 sweetie” “ey : ee re rare: Se re a am wok ad ay saat a primarily concerned with the low-pass case since the high- pass case is easily derived. LINEAR FILTERS A system is said to be linear if for all inputs f(t), g(t), and constants a, b Slaf(t)+b9(t) l=asly(t) l+bSlo(t) ] By superposition, these properties extend to any finite num- ber of input functions. The input and output of a filter can be related by a differ- ential equation, the solution of which gives the output for any input. Notwithstanding, the differential equation description in many cases is not the most convenient for design purposes. More convenient modes of describing a filter, which make use of outputs produced by special types of inputs, employ the following functions: 1. The weighting function. 2. The frequency-response function. 3. The transfer function. The response of a linear filter to general types of inputs may be described by its weighting function which is definea as the response of the filter to a unit impulse function after a time t has elapsed. The weighting function W(t), frequently called the “impulsive response" of the filter provides 4 complete characterization of the filter for W(t) vanishing when + 7/2, then Gey ee R(t) = aT T cos(2nyt) at fo) a(t) = (ar) sin( x7) (13a) Equation (13a) gives a very good approximation of the fre- quency response of the eyually weighted running mean. In gereral, the frequency-respouse function R(*) expresses the relutive amplitude and phase of the input and Output as a function of frequency, and is cefined only for stuble filters. Since the weighting tunetions for the equatly weighted running mean sre even, phise shift is eliminated except ror 180° shifts after the lirst zero crossing of the frequency axis. Bevause of this 180° shift, undesirable oscillations occur Which introduce high frequency ripples into the output. This behavior of the rfrequency-response function beyond the first zero crossing constitutes the Significant disadvantage in smoothing with equal weights. This can be seen by inspection of the curves in figure 1. A brief discussion of the coordinates used in plotting these curves may be instructive. In requiring the weighting function w(t) to be even, the frequency-response function R(f) becomes a pure, real quan- tity. A further condition that the mean or the original time function is preserved requires that the sum of the weights of the weighting functionW(t) be equal to unity. It follows from this condition and equation (11) that the value of the ordinate of R(t) is unity at cero frequency. The frequency f is plotted as the abscissa in cycles per time interval between data values. This time interval is called the data interval, and frequencies are expressed in cycles per data interval in discussing equally weighted running mean and Gaussian frequency-response functions. From a study of the curves for *he equully weighted running mean type filter in figure 1, a good idea can be obtained of its departure from the ideal low-pass {filter with the same = aie a nathlpel a es Oe RNR ASD ais alec tg ie Breet? ieee ' F 5th ETH a sat speed + ate eis iach eee a aut sett yjore bows “8 x cP) Wii eone® Pe re ives ‘ : tet pete i: i ee hae? b ingles : uo t en at bh pits bi 10 ae AC TAT CLE ES IN FREQUENCL RESPONSE A(7) ie} 0.02 0.04 0.06 0.08 0.1 FREQUENCY, CYCLES PER DATA INTERVAL, Figure 1. Frequency response of equally weighted running mean weight funct.on compuced by equation (13). cutoff frequency. The cutoff freq.ency f¢ is defined as the frequency at the first zero crossing of the frequency axis by the frequency-response curve. The ideal low-pass filter leaves all frequency components up to the cutoff frequency f¢ unaltered and eliminates completely all frequency components above the frequency f- en em ¥ 2 *O% at oy a rs * ae . ; Sade bans uma ae. rece sek “Mega ‘Usdyad. Ed) aad Ye aceon, sau aig een A brief discussion of figure 1B will reveal the nature of the departure of the equally weighted running mean filter from the ideal low-pass filter. The graph in figure 1B shows the frequency-response curve with cutoff frequency J, equal to 0.0196 cycle per cata interval. At frequency 0.012 cycle per data intervel, the rrequency response is 0.5 or only 50 per cent. This implies that the filter has removed 50 per cent ot the contribution associated with this frequency component in the input data, as compared with the ideal filter (with the same cutoff) which would puss the frequency component at 0.012 cycle per unit data unaltered. Equation (12) shows the significance of WN as related to the total number of weights (2+1) in the filtering function. The curve in figure 2 gives a graphical description of the cutoff frequency fe as a function of ¥. The cutoff fre- quency is seen to decrease as number of weights in the weighting function increases and, in particular, as V increases. EQUALLY WSIGHTED RUNNING MEAN OF (2 4 + 1) CONSECUTIVE TERMS ft, = CUTOFF FREQUENCY Watts R(s)=% + 2). Wy, cos(2xyk) kL = (2 +1) 4¢, CYCLES PER DATA INTERVAL Figure 2. Variation of cutoff frequency f, with W for the equally weighted running mean filtering function. The curve indicates how the cutoff frequency 7, decreases as NV increases. Note that for NV greater than 6C decrease in fo is not very sensitive to increasing NV. 5. Spe et RNR penemrremeene remeron CENA PDS TO NCR RAE 2 A ER AR fa | Om etree a 5 4, / MES YL Leta IRR ah TRA iA FOE ANLS Sg Bg WAS tea y Vee 1) ROMS Dab mA Biro a ig Br el oe WiC OLR HAE: Diag iss Owe: . eeveee reas No ets nen Cont icine ith ig ata inagE 16 coder FEaia Bees 40 ee <5. Care ‘Sue: eine. ha “s ei hogas oth ‘gots . eaetdgant ee, he Smt Sapte Se Be MAE s a cot an ees ate # the expression reduces to fo} w(t) = 2 f R(f)cos2nft df : ( ie) which is observed to be the Fourier cosine transforms of R(f). Here the frequency response can be specified and the weighting or smoothing function computed. If one specifies R(f) with S) a tt hb (2) WA yy WA Q =0 foo (19) then u w(t) = 2 ce leos (2xft) af (20) W(t) att (xt) sin 2x Oe The chief disadvantage of this smoothing function is its slow damping which renders it impractical for many important purposes. Furthermore if this function is truncated at some convenient distance on each side of tne origin (a necessary procedure in most practical cases), the frequency response of this smoothing function departs significantly from the desired response at most frequencies. The design of a low-pass numerical filter which eliminates many of the undesired properties of those filters or smooth- ing functions discussed above has been achieved vy determin- ing a set of weights ¥, such that the actual frequency response of the filter defined by equation (19) will approx- imate best in the least square sense the ideal frequency response. In the design of this filter the weights W, are determined subject to the following conditions: Poe, 1. The phase shift must be identically zero for all frequencies. 2. (2NV+1) weights are to be used with ¥, = W-k. 3. SEs & earl PAN | QRS | A aie mmaroeertiny Ee eee Ga i ss See ne Se fC RR REAPS [eeeertone ae] 0.001 Sa 0.0005 0) 10 20 30 i) 50 60 70 FREQUENCY, CYCLES PER WEEK Figure 11. Spectral density function (variance per unit band) versus frequency. The graph was obtained from the data used in plotting figure 14 after filtering. The 14-cycle-per-week component has been practically elim- inated leaving the 7-cycle per week component unchanged in shape and magnitude. i < { } eS a alia on 4 el oT, Die i erie A, A SRE i Mn SO RR nan? AR en = ee Sw nn ae SUMMARY AND CONCLUSIONS Three types cf statistical filters have been discussed relative to their effectiveness in performing smoothing or filtering of data in time series. 1. The equally weighted running mean type of (2N+1) consec- utive equal weights, has a frequency-response function which decreases smoothly down to its cutoff frequency fg¢ which is determined by NW. This filter is computationally simple and has a relatively sharp cutoff, but its frequency response oscillates above the first zero crossing introducing un- desirable ripples in the data. This filter is less critical than desired for many purposes. 2. The Gaussian smoothing function, though devoid of the oscillatory defect in the above type, has a frequency response which drops smoothly approaching zero asymptotically. This function does not have a cutoff but for practical purposes a cutoff may be arbitrarily defined as the frequency for which its frequency response is 1 per cent. With weighting functions of the same VN, the equally weighted running mean type has a much sharper cutoff than the Gaussian type. Where the demand for sharp cutoff is not severe, the Gaussian smoothing filter may be used to adventage. 3. In the equally weighted running mean and the Gaussien types of filters the weighting function is specified and from it the frequency response function is evaluated. It is possible to reverse the procedure, by specifying the desired characteristics of the frequency response and from these conditions determining the corresponding weighting function. The weighting function w(t) is the inverse Fourier transform of its corresponding frequency-response funct.on (see equa- tions (6) and. (7)). This type of filter discussed earlier specified a gain of unity and zero phase shift for all fre- quencies. To further improve the fidelity ot this filter, the frequency-respons2 wus terminated at its ideal cutoff frequency, To, by sine termination, and the weights further corrected to insure unity gain at zero frequency. By a proper selection of the parameters r,, hk, and ¥ (see list of definitions) filters with maximum absolute error less than 1 per cent have been designed. Weights for 118 such filters are given in the Appendix. Computer programs have been written for the Burroughs Data- tron 220 computer and were used in obtaining the numerical results for all filters discussed in this report. ae ELT LORELEI AY RR PARA NT A = wally Bete aR ANE NB eb A atk ah fi A ee ers eee Serie PPPS: fas sian ddee ws 7 ase autres. Ee rer te <¥ be a: | RSET EE REFERENCES 1. James, H. M. and others, Theory of Servomechanisms, Chapter 22, McGraw-Hill, 1947 2. Bendat, J. S., Principles and Applications of Random Noise Theory, Chapter 1, Wiley, 1958 3- Goldman, S., Information Theory, p.67-71, Prentice-Hall, 1953 4. General Electric Company Document No. 57SD340, Frequency Domain Applications in Data Processing, by M. A. Martin, May 1957 SEA ST re a LE tp one rn pnt gi Te Se bee Sun: -§ u ul DEFINITIONS the filter input. the filter output. frequency in cycles per unit time. cutoff frequency in cyeles per unit time. sampling frequency (rate). an integer defined by the total number of weights (241) in the weighting function. an integer whose range is 1, 2, ...WM. continuous weighting function variable time parameter. weights of the discrete weighting function. frequency-response function which relates a sinusoidal input to the output that it produces. variable in the smcothed time series. flitering interval. data interval. normalized frequency ratio defined by Site where J is in cycles per unit time and Jf, is the sampling rate. normalized cutoff freaueney for the ideal filter defined by the ratio f,/f, where fg is the cutoff frequency in cycles per unit time. the normalized cutoff frequency ratio for the approximate filter. maximum absolute error in the filter gain from zero frequency to the normalized cutoff r,, and the frequency range between the first zero crossing and the frequency limit, r= 0.5. Note the range of r is from r= 0 tor= 0.5 for the filters @iscussed.. rr er mete, 0 Saat ea Bai rene Lipaitage ah Sop Bet ete nay Toe “ iis anes I La He OR ¥= < op a ne a a ened at hee He ee 30 hk = variable parameter which permits variation in the slope of the sine termination and is effective in diminishing the oscillations beyond the first zero crossing of the frequency-response function. (r) = frequency-response function as a function of the normalized frequency ratio r. | | Wass APPENGIX: FILTER DATA Table 1 contains design parameters Toe» By Tags Fy, and NV. Various filter parameter combinations are listed relative to increasing values of Te in the following order 0.01, 0.023, 0.05, 0.08, 0.10, 0.20, and 0.30, and the subgroups are listed relative to increasing values of h. For any particu- lar subgroup it is observed that as V decreases the value of the absolute error F increuses. The filter number corresponds to the arrangement of 118 sets of weights given in table 3. Table 2 gives the filter parameters Tas 2, Tag #, and M along with the corresponding frequency-response data r and A(r) for filters numbered 1 to 4 inclusive. Table 3 gives the filter parameters To, hy Tac, F, and V ana the sets of weights for all the filters which are numbered to 118. Given the filter parameters stated above and the corresponding sets of weights, the frequency-response data are not necessary for designing the filter. An example of one procedure for using the tables for filter design is as follows. Suppose one has a set of data sampled 12 times per day and it Is desired to filter the data re- taining all frequency conponents below 25 cycles per week and rejecting higher frequency componerits. Also, there is reason to believe that no frequency components exist in the data higher than 0.5 f,. Then, f, = 0.5(12)(7) = 42 cycles per week. L.. Calculate Tr, from the relation qd ' it} ae Q and 25 Toe = Waa) 0.298 é. Select the value in table 1 nearest r',. In the case considered, ™- = 0.3. Then fe= (0.3)(34) = 25.2 cycles per week, which is the ideal cutoff frequency fc for r, = 0.3. 3- Finally select the smallest »% (the sharpest cutoff) and the smallest ¥ consistent with the maximum error in the gain Sa a ee LCD ener enum: 31 \ wy des | sy * By 4 ANE § om Se BL Saye ow Stgspae sie. i ai Oe, eu Can oh ay, hy Wout Sie | A aaent es 7” 32 which can be tolerated. In table 1, re = 0.3, h = 0.03, and N = 20 will give the cutoff normalized frequency namely Tac= 0.355. The absolute error 2 = 0.006 is seen to satisfy the gain requirement. The corresponding Tre (the frequency of the first zero crossing is (0.355)(84) = 29.8 cycles per week. However the amplitude of the frequency components between f,.and fgg fall off rapidly in magnitude, the rate of fall depending on the parameter h. Tye various filters given in table 1 and corresponding weights in table 3 will satisfy the conditions for many prob- lems. Table 1 is limited and, for some problems, desired r¢ values are not sufficiently close to any given in the table. Suppose in the example given above one desired to retain all frequency components less than 3 cycles per week and eliminate all frequency components greater than 3 eycles per week. The calculated 7. = 0.0357. The nearest value of re in the table is 0.03 which gives the cutoff frequency f, = 2.52 cycles per week. If greater precision is desired, a set of weights may be computea by equations (21) through (24) using the appro- priate r, towetner with the appropriate vaiues of A and NW. Ieee er sme ep a ae te a cepelagerint etr tnt igs hatatnd dre a ‘ ¢ 68 u Teak oh : cat ERNE Ewe rep rr TABLE 1. FILTER DESIGN PARAMETERS The ac.uul cutorf frequeucies, Tac, and maximum errors, 3, are lisied corresponding to specific choices of eutorf fre- quency (ro), parameter A, and the number or Weights (241). The values ct the weights for a particular choice may be found in tuble 3 in which the filter numbers are the same as in this table. Filter No. NM au LOO 2 6°) 3 60 4 100 2 TO 6 50 T TO, 8 50 9 30 10 20 il TO 12 50 13 3 14 20 15 10 16 3c aly e 18 10 19 30) 20 30 el 20 22 10 23 4 2k 3 25 60 26 90 et bO a 4o 2y 30 £ r ac 0.0046 0.02T5 -008 -0325 -0125 -O2TS 0.0001 0.075 -0003 -065 -001 -085 0.00007 0.145 -CCO1 “135 -COL -12 -006 -115 0.00004 0.195 -COOl -185 -00064 -165 .002 -105 -Q00 -175 0.0004 0.205 -O0O1 -205 -O045 -205 0.000005 0.405 00004 415 -0003 405 -OOL Lo5 -003 “OS 0.004 0.425 0.005 0.0475 0.00006 0.095 -0005 -105 -OCz -115 -OO47 -085 0.03 0.08 Q.20 0.03 > Se ear aoe y ert NAT ai oa mi No. N 30 70 31 30 32 20 33 10 34 60 35 30 36 20 37 10 38 60 39 30 4O 20 hi 1u 42 ¥(0) 43 30 uh 20 os) 10 46 4 7 70 £8 60 4g 90 50 50 51 30 52 20 53 TO 54 ho 55 30 56 20 5ST 60 58 30 5 2c 60 10 61 50 62 30 63 20 64 10 34 Tyre OPIS Sr a 7 ° -0000C6 0006 -10 -O5 08 -10 055 Toc ie ae Y ' io, ie, cra. Noemi Aes a Ole tat HN alls Ae aoa aC 1 es se cca LVR Ie rr a £ Q.000007 -O0007 -0002 -001 0.01 0.000007 -C0006 -Q002 «COL 0.20 0.03 0.08 0.10 0.03 0.08 0.20 baa 0.08 35 ROE GAL: Laon wa ahs sis 5 ti Ae oe Nii i Shag ek NN RNY % ft Tea Am fe Filter 36 No. K 99 60 100 20 10l. 80 102 30 103 20 104 10 105 50 106 30 107 20 108 10 109 60 110 3c 111 20 112 90 113 740) 1b 10 115 gO 116 50 NG 20 118 1 (e) E .0006 .0038 .00003 -0003 -O01 -006 .00006 .0003 .00098 .0038 .0002 -003 -006 -O00001 .0004 .006 .000004 . 00007 .0008 .004 0.275 2229 0.395 365 0.395 395 0.395 0.375 ~355 0.465 465 0.495 0.495 0.03 0.08 0.20 0.30 TABLE 2. FREQUENCY RESPONSE DATA FOR FILTERS. THROUGH 4. FILTER NO. 1 - rz = 0.01, A = 0.01, W = 100, Z = 0.00h6, enna 0.0275 r R(r) r Rfr) r R(r) 0.000 1.0000 0.215 0.0000 0.430 -0.0001 .005 0.9960 £220 36-0. 0001 ~435 6.0000 .010 1.0019 6225 0.0000 440 -0.0001 .Q15 0.8534 -230 -0.0001 AS 0.0000 -020 0.5008 -235 0.0000 450 = -0.0001 025 0.1448 -240 8=-0.90001 455 0.0000 .030 -0.0001 -245 0.0000 460 -0.0001 .035 0.0019 250 -0.0001 465 0.0000 -O40 -0.0014 .255 0.0000 470 = -0.0001 -O45 0.0010 260 -0.0001 ATS 0.0000 050 -0.0008 -265 0.0000 -480 -0.0001 +055 0.0006 -270 8=-0.0001 «485 0.0000 -060 -0.0005 -275 0.0000 -490 -0.0001 -065 0.0004 .280 -0.0001 495 0.0000 .07O -0.0004 .285 0.0000 0.500 -0.0001 -OT5 0.0003 290° -0.0001 .080 -=0.0003 -295 0.0000 .085 0.0002 -300. =-0.000]. 090 + -0.0002 305 0.0000 -095 0.0002 .310 -O0.2001 -100 -0.0002 .315 0.0000 .105 0.0001 .320 = -0.0001 .110 -0.0002 325 0.0000 .125 0.0001 -330 -0.0001 120 = -0.0001 -335 0.0000 .125 0.0000 -340 -0.0001 -130 = -0.0001 2345 0.0000 ©4135 Q.0000 -350 -0.0001 -140 = -0.0001 -355 0.G000 145 0.0000 -360 -0.0001 .150 -0.0001 365 0.0000 .155 0.0001 -370 -0.0001 -160 -0.0001 -375 0.0000 -165 0.0001 -380 -0.0001 -170 =©-0.0001 385 0.0060 -175 0.0000 -390 -0.0001 180 -0.0001 .395 0.0000 ~185 0.0000 -400 =-0. 0001 +190 =-0.0001 405 0.0000 .195 Q.CO000 410 -0.0001 .200 -0.0001 415 0.0000 -205 0.0000 420 — -0.0001 0.210 -2 0001 0.425 0.0000 Se i i ve o FILTER NO. 2 - r,= 0.01, hk = 0.01, w = 70, F = 0.76, $US MRR Tae = 0-0325 r R(r) r R(r} ; 0.00 1.0000 0.43 0.0001 ; 01 0.9967 4h 0000 : 02 5006 45 -0.0001 i 03 0022 46 0.0001 ‘ Ob 0010 47 0001 } 05 0009 48 -0.0001 06 0001 4g 0.0000 : O7 -0.0005 0.50 0001 08 0.0000 09 .COO4 10 .0001 11 -0.0003 12 0.0002 13 .0002 14 -0.0002 15 0.0000 16 .0002 17 -0.0001 18 .0002 19 0.0002 20 .0001 21 -0.0002 22 0.0001 23 .0002 2h -0.0001 25 .0001 26 0.0001 27 .0000 28 -0.0001 29 0.0001 30 .0001 31 -0.0001 32 .0000 33 0.0001 3h -0.0000 : 35 -0001 : 36 0.0001 37 -0001 38 -0.0001 39 6.0000 : 4O -0001 4D -0.0001 0.42 0.0001 ; | j 38 i i ELASTOMERS ALN LTTE TL AL od i ni. i ne ¥ merit. oF TTC marion sey nia eee te ee ten rm eo er ee a ran at FILTER NO. 3 - rz = 0.01, h = 0.01, M = 60, F = 0.01, Taq 2 09-0275 r R(r) r Rr) 0.00 1.0000 0.43 0.0002 -O1 -OO11 44 -0.0005 .02 0.5037 “AS 0.0010 .03 -0.0058 46 -0.0007 -O4 0.0084 UT 0.0005 -05 -0.0011 -48 -0003 .06 .0030 «49 -0.0006 .O7 0.0046 0.50 Q.0010 -08 -0.0036 209 0.0017 -10 .0007 S11 =0.0021 -12 0.0027 13 -0.0018 «14 0.0007 215 .0009 16 -0.0016 -17 0.0019 18 -0.0011 19 0.0002 -20 -0010 .2l -0.0013 -22 0.0015 .23 -0.0007 ook .0000 25 0.0010 26 -0.0012 27 0.0012 28 -0.0004 29 .0002 30 0.0010 31 -0.0010 32 0.0010 33 -0.0002 34 .0003 35 0.0010 36 -0.0010 = 37 0.0008 38 .0000 39 -0.0004 4o 0.0010 41 -0.0008 0.42 0.0006 : 3 a i +8) fe TE SS SS EH ot BC en ee _ a 1 A ACR RISE A ED ik MT BPS ae gs at elie ¢ a ome tom 2 Efe: ¢ atom oe SEB a ub ea Tatidy Ween Te reap mons An Seb Maan een See heals FILTER NO. 4 - r, = 0.01, 2 = C.03, ¥ = 100, 0.0001, Tac. = 0-975 Rr) 1.00000 1.00010 0.93300 -TC00 . 50000 -25010 .06710 .00000 -9.00010 -00008 -00005 .00004 -00003 .00003 -00002 .00002 .00002 .00002 -V0001 «00001 -OO0OOL -00001 -00001 COOOL -Q0001 -00001 -O0GO1L -Q0001 .00001 .000C1 - ,00001 -O0001L .OO00L -00001 r Rr) 0.43 -0.00001 4k -Q0001 45 -OCO01 46 -OCOOi 47 -09001 48 -O0001 wg -O0001L 0.5C -0.00001 car ac a gl opr ean no eg ns pee nae bi SANG Ra Nt ft 3 2 ‘ wae 4 : ort eneN as TABLE 5. VALUES OF WJIGHTS RESULTING FROM THE SETS OF - PARAMETERS GIVEN IN TABLE 1. FILTER NO. 1 - rz = 0.01, % = 9.01, ¥ = 100, # = 0.006, Tao = C0275 k Value of k Value of k Value of Wy Wy Ws, 0) 0.03998 36 -0.CO467 fio) -G.00002 1 -03986 39 -00433 77 -00000 2 .03950 40 -00394 7é 0.00001 3 03091 4d -00353 19 -GO0O4 4 -03€09 42 -00310 60 -00006 5 -03795 43 .C0265 81 -00009 6 -03561 4h 00221 82 -O0011 T -03438 4s -00178 83 -00014 8 -032738 k6 -00137 reds -00016 9 -03102 LT -00098 85 -00018 10 -02914 43 -00063 86 -00020 11 02714 49 -00030 87 -00021 12 -02506 50 -COC02 88 -00021 13 02291 51 0.50023 89 -00021 14 -02072 52 00044 90 -00021 15 .01652 53 -COO60 gl .00020 16 .01622 54 -C0073 ge -00018 17 -O1415 55 -00082 93 -00017 18 -01203 56 -00088 94 -00014 19 -00998 ST -0009) 95 -00012 20 -O0011 58 -G0091 96 -00009 21 .CO615 59 -00088 oT .00007 22 -CO4LO 60 -00084 98 .00004 23 -002T9 61 -C0078 29 -00000 2h -CO131 62 -COOT1 100 -0.00002 25 -0.C0002 63 .6C063 26 -CO120 . (ours -0005% 2T -00223 65 -00046 28 .00310 66 -00037 29 .00302 6T -60029 30 -OO440 68 - .c0022 31 -COLG3 69 -06916 32 .00513 FO. a. -00010 33 .005 20 val -00006 34 -00536 Te -cOo02 35 -00531 3 -0.00000 36 .00518 Tu -00001 37 -0.00496 165) -G.00002 bi eee et ee Bere ee FILTER NO. 2 - Po WO DOAHAU FWWFO. = 0.01, A Tag = 09-0325 Value of M;, 0.04002 .03990 -03954 -03895 -03813 -03709 -03585 -O3442 .03282 -03106 .02918 -02718 -02510 -02295 .02076 -01856 -01636 -01419 -01207 -01002 -00805 -00619 OO4LK -00283 -00135 -00002 -00116 .00219 -00306 -00378 -00436 -00479 -00509 -00526 -00532 -0C527 -00514 00492 -004.63 00429 00390 00349 0.01, N = 70, F = 0.006, Value of Wy. -00306 -00261 i iy t i c oo WRB OA Ty AAS FNS Ot ie ee j fey 7 FILTER NO. 3 - rz = 0.01, h = 0.01, ¥ = 60, E = 0.01, ps 0.0275 k Value of k Value of ; 0 0.04010 ho ~0.00298 { 1 -03998 43 -00254 8 2 .03962 Ay -00210 § 3 -03903 45 -00167 i 4 -03821 6 -00126 t 5 -03717 47 -00087 : 6 -03593 48 -00051 i Ti -03450 kg -00019 : 8 03290 50 0.00010 i 9 -03114 51 -00035 : 10 -02926 52 -00055 } 11 -02726 53 -00072 12 .02517 5k .00085 13 -02303 55 -00094 14 -02084 56 .00100 i 15 -01863 5T -00100 16 01644 oe 00100 17 01427 59 0C100 | 18 01214 60 00100 : 19 -01009 i 20 -00129 i 21 -00627 s 22 -00452 : 23 .00291 j 2h -00143 : 25 .00010 H 26 -0.00108 ; 2T .00211 ratets 28 -00298 29 -00371 30 -00428 31 -OO471 32 .00501 33 -00519 34 .00524 35 .00520 36 .00506 37 -OOL84 38 -00455 39 -O0h21 : ko .00383 j 4d -0.00341 8 43 : 4 Sy Ga en ee st paiires Was Sane ae orl i Ree iy : 4d FILTER NO. & = rp = 0.01, A = 0.03, ¥ = 100, F = 0.0001, WOON aN FWHFE O Value of Wy 0.08000 -07889 -07564 -O7046 -06364 -05560 -O4681 -03773 -02883 .02052 -O1314 -00691 .00200 -0.00165 -00403 .00530 .00566 -00535 -00459 -00361 -00257 00164 -00089 . 00037 .00009 .00000 -00007 .00022 00041 .00057 -00068 .O0CT2 -O00EY Tac = 0-075 k Value of Wy -0.00002 .GCO0O7 -00012 -00014 -O0015 -00013 «00003 -O0005 -QOO000 0.00004 - 00007 - 00009 00009 -OO0O00T »00005 .00003 ~GOOOL -0.00001 »00002 -O0002 -~OOO001L 0.00001 -00003 -OCOO4 -O00006 -00006 -OO0OT .00006 -O00005 -OGCO4 .00002 -OO0O1L -O00000 -0.00090 O.00C00 ~QOCOL .COGO02 -O0002 .00003 -OOGO4 00004 0.00003 k Value of Wy 0.00003 -Q0001 -Q9001 - 00000 -0.00000 -O00CO1L -00001 -00000 = bas leet * LO. a 7 lg co ag AD oh. 7 : ie 4 inl Value of ay 0.08000 -O7520 -Of505 -0 .0CU0F -O0C22 -OCO+C OCO5 7 -OOR72 -00CS5 .00052 ~OQCO55 -O0030 -O00Le 00004 0.00004 -OO007 -OCCOT 0.00004 G oO tal [S) (Ss) wy > ae) NO emt Gn a a neY om re on cop nantes cos ma ag a ee yor enn pe aS eS FILTER NO. 6 - r, = 0-01, 4 = 0.03," = 50, F = 0.001, POCA ATS SN ER TE TRS RESET Fan = 10.065 k Value of & . Value of ' af * x re) 0.08c02 ho 0.00000 1 07891 43 ~0.00005 2 OT567 He -00009 3 07048 SS -00012 4 06366 46 -00012 5 05563 47 -GOO11 6 04633 LS -0000T T 03775 43 -00003 8 02885 50 0.00002 g 02055 10 01316 11 -00693 12 -00199 13 -0.00163 14 00400 id 00528 16 00564 17 00533 18 -00457 19 -00358 20 -00255 al -00162 22 -00087 23 -00635 ok .00006 25 9.00002 26 -0.00004 2T -00C20 = 28 -00038 29 -00055 30 .00066 31 .00070 2 .00067 33 -00057 34 00044 S -00028 36 -00014 37 .00002 33 0.00005 39 -C0009 4o -00009 4l 0.00005 Pai ces age erm oS ea SN SUR Nar 2 NE eS Ae ESTO NN vale ee vel seu Tere MENT aoe i FILTER NO. 7 - r,= 0.01, 2 = 0.055, W = 70, F = 0.00007, c Tac= 9-155 A Value of k Value of W, Wy. () 0.13000 he -0.00003 ak -12499 43 -00005 2 -110890 dy -00005 3 -O9C04 ks -00003 4 -O6527 46 .00000 5 04225 a 0.00002 6 .02134 48 -00003 T 00694 49 .00002 8 -0.00221 50 -Q0000 fe) -Odcle 51 -0.00001 10 -OC035 52 -00002 17 004859 53 -00001 12 00234 5k 0.00000 13 -OC0s1 55 -00002 14 0.C0015 56 -00003 15 00015 ST -00002 16 -0.000322 58 -Q0001 17 .00CS1 59 .00000 18 -00105 60 -0.00000 19 00027 62 . 00000 20 -OOCe7 62 0.00001 a1 00031 63 -Q0002 22 -OCOOT 64 -0C002 23 0.00000 55 .00002 oh -0.00008 66 .00002 25 C0022 67 .Q0001 -9 .00032 68 .00000 oT .00034 69 .GO000 28 -OOCET 70 0.C0000 29 20015 30 “B000% 31 0.cOOdl 32 -0.0C001 33 -OCEte 34 C0011 35 00014 36 .COGI2 37 -OCCOT 38 -00002 39 0.00002 Xe) -O0002 ky -0.00000 er ne ee no rer 4 4 | =e aye Scare. ea AiR BASE UB aaah) Jy eg, Weaiete CERES a Ho eb ae FILTER NO. 8 - -, = 0.01, h = 0.055, N= 50, F = 0.0001, Fao 0.135 k Value of k Value of i, We (6) 0.13000 ho -0.00003 Al .12500 43 -00005 2 -11086 yy -00005 3 .09004 by -00003 h -06597 46 .00000 5 -04226 LT 0.00002 6 -02195 48 -00003 T .00694 Hie) -00002 8 -0.00221 50 -Q0000 9 .00616 10 -00637 11 -00459 12 -00233 13 00061 - -- 14 0.00018 15 -0G016 16 = -0.00031 17 -00081 18 -O0105 19 .00097 20 -00666 el -00031 22 -00006 23. -0,00001 24 -0.00007 25 .0%021 26 .Cy032 27 -00034 28 .00027 29 .00015 30 -00004 31 = 0.0G001 32 ~=-0.00000 33 00005 34 00001 35 .00013 36 .00012 37 .00007 38 .00002 39 0.00002 40 00002 41 0.00000 aa Ae SETAE ne UES A ag Ar SE pee a egg a RR A A pul : Bios a ? FILTER NO. 9 - re = 0.01, 2 = 0.055, W = 3C, EF = 0.001, FILTER NO. Mr oO QO ON Gm FY = The = 0.125 Value of x aie 0.12999 16 -12498 17 -11084 18 -09003 19 -06595 20 022k eal 02193 22 .00092 23 -0.00222 eh 00618 25 .00639 26 cohé1 eT -00235 28 -00063 29 0.CO0O1T 30 0.00014 10 =<\7e =0-01, ® =.0.955, r = 0.115 ac Value of k ws 0..7389 IB - 12456 12 -11075 13 -03993 14 -C6586 15 -04215 16 -02184 17 .00683 18 -0.00232 i9 20027 20 -G.00648 Value of 20, F = 0.006, Value of hg eos os ham Uae Braye. MURIEL SETS TEEN er er sca AER tee ON ew eee FILTER NO. 11 - ro = 0.C1, 4 = 0.08, W = 70, F = 0.00004, Tac = 9-499 WO ONAYU FWHrFO Se a ni ee anne ot menenersaner recent petimciphlameah wre! oS icmannibe piven) en ts So en ee an eee ap 0.18000 -16651 -13070 » 08432 -O4069 01020 -0.00467 -OO7ET 00446 -000E4 0.00063 -00G012 -0.0003%0 -O0C127 -OU0ET rage RTOPIEY cece, eo AR een em mar k Value of Wy ho -0.00003 \ 43 -00003 ky -O0001L 4S 0.00001 46 .00001 7 -0.00000 48 .00001 49 -00001 50 0.00000 51 -00001 52 -00001 53 . 00000 54 -0.00001 55 . 00000 56 0.00000 57 -00001 58 .00001 59 -00000 -0.00000 61 - 00000 62 0.00001 63 -O0001 64 -00001 65 . 00000 66 -0.00000 6T 0.00000 .00001 69 -00001 70 0.00001 Ba, al 2 mee a 2 sine y! bes epee Sonik + SH 0 EN RS AREY aire ee eee Sener nce FILTER NO. 12 - r, = 0.01, h = 9.08, M = 50, E = 0.0001, Rees 0.185 k Value of Wy, fe) 0.1800C 1 -16652° 2 13070 3 -08431 4 -04090 5 01620 6 -0.00487 T -OO767T 8 -OO4L8 9 -00084 10 0.00063 11 -00012 12 -0.00090 13 -00127 14 .00086 15 -00024 16 0.00006 17 -0.00008 18 -00035 19 -O0044 20 -00030 21 -00009 22 -00000 23 -00006 24 .00017 25 -00020 26 -00013 = -00003 28 - 00000 29 .00003 30 -Q0009 31 -00010 32 -00006 33 -00001 3h 0.00001 35 -0.00002 36 -00005 37 -00005 38 0.00002 39 -0.00001 ko 0.00001 ki -0.00000 k Value of 51 FED SRC OATES, EEE TN Spe RIR I ASR TARE tl MGSO RISE # v 3 “ Rear ee te gill See nin ype oe: RIS 52 FILTER 1G. 13 - ~ 5 Neg G Ss Ec Bw WMAAW Fw he oO 0.17999 - 16650 - 13069 -08430 -04059 -01019 -0.0C483 -OO7TES 00449 -00085 0.00062 -00011 -0.00091 -001 25 -00088 -0.00025 0.00005 0.20009 - 00S 36 -COTL6 -cOCI2 - 20010 -SOCOL RECO 8 ( 20018 -OOo2h COOLS, -O0GOL -OCOOL rc ow -9.00610 FILTER NO. 14 - r,= 0.01, 2 = 0.08, ¥ = 4, z = 0.002, ~ oO OO MN OU! £1) Fb Tae = 0-165 Value of Wy 0.17995 - 16646 .13064 08426 -O4084 01015 -0.00492 00772 00454 -00090 0.00057 See eh a pe a i Sut paeasca one ere 9.00013 205G60 - 99050 -O0g3s es Net oSeee da bs. otters nie oi SEA eee aU a wae Fe i | “a ‘ i a ii > oy aay - i ely. Se a a ee os nn ORE r 0.08, ¥ = 10, F = 0.006, FILTER KO. 15 - 7. = 0-01, % Fun = O-LTS x <3 * q. 2 SOL Value of wy, Wy -0.00528 -O081d - .00500 -00136 C.0CO11 OW @=) OV ° ¢ 4 C we bY MEW EH SC. © ¢ ra ra) FILTER 40. 16 - re = 0-01, % = 0.1, ¥= Fac — 0-205 0, B= 9.00003, lo *“ Value co? k Value of ‘ Wi, js be a Qo Ov i (oe) aS pe ow 4 4) -0.00013 -GO00c+ -00017 2B ONO OA OVI FWhYrH Oo 22 -00003 Ez .00G01L ee -OC0i0 25 .00C1L2 a ce .OCCEG ia BF -OCCGL 12 23 -000CE 33 és -COGOT 14 =-0.GU516 30 -Q0GEE 15 =0.000ES iwi) (Ss) soe Saar macho ma eae 5. av Ray's! ee ot aes at RR RR A NR SO FILTER NO. 17 - r, = 0.01,” = 0.1, ¥ = 20, F = 0.001, k Value of zk Value of wy Wy 0 0.2198 hn -0.0012T = 17532 1 -00037 2 -12416 13 0.00009 3 CES 1h -0 .00019 & 201515 15 -00053 5 -0.0CZ50 15 -OOCkL 6 -COTES 1T -00013 T COLE 18 -00C0z ra} O .COCET 19 -00016 9 -COO1L 20 -C0028 10 0.00123 FILISH 50. 18 - r, = 6.G1,4 = 0.1, ¥ = 10, F = 0.006, Tee = 0-205 k Valte of k Value of wy W;, fa) 0.21565 6 -0.0079T 1. -17506 ites -00239 2 15354 8 0.00056 3 CASS 9 -0.00020 4 -S1ick i0 -O0160 5 -0.C0691 54 feat me or ne neers ny FILTER NO. 19 - rz = 0.01, A = 0.2, ¥ = GO, F = 0.000005, = Fon = 0.405 k Yelue of k Value of 4 *, wy a 0 0.42000 42 0 .GO000 2 1 ~ZELES 43 6.c0000 i 2 -02976 by 6.50000 3 0.62215 45 -22000 ' 4 9.00225 46 0.COCOO 3 5 -9.00131 LT -0.C0000 : 6 -O00T4 48 0.00000 ; Ge 0.00023 kg -0 .C0000 § 8 -0.00073 50 0.20006 i 9 0.00014 51 -00000 i 10 ~0.00030 5 -0.GO0000 1) -09011 53 C.000CO 12 -00003 5h -0.05000 : 13 -00018 55 0.00000 i 14 ©.00002 5 -C0000 i 15 ~0.99012 57 0.00000 ae | i6 .00003 53 0.Coo0c H Vy -00003 59 -G.CO000 ae 18 -SCOOT ©.G0G00 I 19 @.00000 | 20 -0.99006 ; 21 -OO001 ; 22 -GO003 i 23 -50003 i 2h -00000 i 25 00003 F 26 -C0000 : oT -OCO0E 5 28 -00001 4 29 -00GCO : 30 -CODOL i 31 0.90000 bo 32 0.90001 een 33 -GOCCO i 34 -0G000 E 35 -COCOl A 36 G.90000 § 3T -O.00001 5 38 -O0K00 4 39 -000G0 ‘sO -G0000 iL ©.00000 22 FILTER NO. 20 - r,= 0-01, A = 0.02,.% = 30, B= 0.00064, wanes ene emp me ern emebae O- G.52069 16 -0.00003 1 LED ig -COCCL i 2 -O2776 1s -GOOOT is ENR S SEAS) iy 0.c00Gs0 k G.0GZE5 a -€ .CCGOG 5 COOLS 21 -O000L 6 ~O007% ce 00003 i T C.COCE3 eS -ODU% ' 8 =O CCT ce -CCOSO 9 GsGOOLe CE i 3 10 2.60025 Le -C00GO u COOLr at 052 } ac 4 SKIS «DOES 0.00002 -5 COCL2 He Fw tay PO SRR (eres 38 Bs ee bh WwW FILTER HO. 21 - 7% = G-Oly h = 0.2, 4 = 2, 2 = 0-CO0S, Fac = G.405 k VYeius of & Value of i; Wy ) G Igy al =920001 1 ona pr Osos 2 -O2919 a3 -OQ0L9 3 =G 01215 1s. 0.05001 i GS -CGZE4 a5 —G. 006213 | 5 “GOGLZ “16 .O00G4 6 20SC75 bees 00604 | T 6 .LCCz2 ie SOOGOS: 8 =G COOTER ae) OL 9 O.612 Ze <3. COCO. 6 = O00EE Ly ee Se ir eee a qenia h my wy ae) Eat outhadl x Phe FILTER NO. 22 - 7% = 0-01, h = Q.2,N = 10, F= 0.001, Wiig 0.405 i k Value of k Value of Wy Ws. ) 0.41992 6 -0.00082 i 1 26457 i 0.00015 } 2 .03969 8 -0.00080 { 3 -0.01322 —" 9 0.00006 4 0.00217 10 -0.00037 5 -0.00139 FILTER NO. 23 - re = 0-01, 2 = 0.2, N = 4, E = 0.003, ios 0.405 k Value of k Value of (0) 0.41922 3 -0.01393 1 - 26387 h 0.00147 2 0.03898 FILTER NO. 24 - re = 0.01, h = 0.2, = 3, F = 0.004, Tac= 0.425 k Value of k Value of Wy Wy 0 0.41964 2 0.03940 iL » 26429 3 -0.01351 a Pag = = 8 SpA A ae a FILTER NO. 25 - 58 x WO ONAwWFWNWrRO o = 0.03, A= 0.01, = 66, F = 0.005, ries 00475 Value of Wy 0.07997 .07910 07652 -07235 .06675 -05995 -05220 -04382 .03511 .02640 -O1799 -O1014 .00312 -0.00291 .00781 -01149 -013595 .01522 -01539 -O1461 .01303 -01084 .00826 00547 .00268 -00003 0.00231 .oohk2k .00570 -00663 .00705 .00698 -00648 .00563 00452 -00324 .00190 .00059 -0.00062 00165 00246 -0.00302 Value of Wy - -0.00333 -00339 -00323 ~ 00289 -00241 -00183 .00121 .00060 -00003 .00046 -00085 .00112 -00128 -00133 -00128 -00115 .00096 .00073 0.00050 2 £ i a Va H $ $ ® a eee PON Pan a NE FILTER NO. 26 - ro = 0.03, = 0.03, V = 90, F = 0.00006, WOAAWUFWHrEO 10 ¢ eee en A ae EO ES, Value of Wy 0.12000 -11678 -10108 *.09313 -07523 -05561 -03614 -01851 -00399 -0.00662 -01314 -01585 -O1547 -01293 -00923 -00530 .00183 0.00074 -00225 -00278 -00257 -00194 -00118 -00053 -00013 .00000 -00010 -00031 00054 -00068 -00068 -00056 -0.00001 Tac = 0-095 k Value of -0 -0. -0. Wy -00000 -00063 .00009 -00014 -OOO1LT .00017 .00013 - 00007 -00000 .00006 -00010 -00012 .00010 -00008 k Value of Wy 0.00001 .00002 00003 .00003 .00002 00001 0.00001 HAI SI Geo Wa aN iS Cais Sle a NS Ia 2 ees aS Lal aay: é x : Val Seer oA ‘ a r MS Hpbi soar” vedi Al ig ae Re gee Rte ee in Sm eemos eae aS / ir a FILTER NO. 27 - ro = 0.03, h = 0.03, M = 60, E = 0.0005, k WO ON AW FWHWrE O Usa 0.105 -0 .00662 -0.00015 Value of Wy -00000 0.00002 ee RR ne ne et eae te FILTER NO. 28 - r, = 0.03, = 0.03, V = 40.F = 0.001, OW MAIHDUFWHFO Tas 0.115 Value of k Value of Wy Wy 0.11999 21 0.00193 .11678 22 -O0117 . 10748 23 .00C52 -09312 2k .00012 -O7522 25 -0.00001 -05560 26 0.00009 -03613 2T .00031 -01850 28 -00053 -00399 29 -Q0067 -0.00663 30 .00068 -01315 31 -00055 -01586 32 .00033 -01548 33 .00008 -01293 34 -0.00015 .00924 35 -00031 -00530 36 .00038 .00183 37 .00035 0.00074 38 .00027 -00224 39 -00016 .00278 ho -0.00007 0.00257 61 ee mn ARETE P/E | s a 5 : : } 4 dll ORE h de WBE ii bts 8 Semel ts Be baie. ey ad! 5) 8 * ee ; a yt fo i Song ey - 4 We The abd i ‘ ¢ RY Aya | 62 WO OAHNAMN FWHWHrFO Tac = 0-085 -0 00665 k 4 PE ; Weyer « or ehe one ERs ae “ fe : ns are if ie UVB LNE oa, Ce SCO Ha 8 Seah LCASRAN Seng ges PaO RENN IE Spee SURE ERR UNE ee SR en arena RR EN OSI id Fo FILTER NO. 30 - rm = 0.03, h = 0.055,N = 70, F = 0.0001, { =) O65 k Value of k Value of i te Wy Wy : fo) 0.17000 4a -9.00002 ' 5 1 -16021 43 -00005 ca | : 2 -13326 yy .00007 : { eee 3 09565 bs .00006 eee 4 -05581 46 -90004 oe 5 -02153 LT -00000 6 -0.00216 48 0.00002 rT 01398 4g .00002 8 .01596 50 ~0.00000 9 -01205 51 .00002 10 -00638 52 -00002 Bon a: -00187 53 0.00000 Aol 12 0.00030 54 .00002 : ! Se 13 -00046 55 00003 a 14 -0.00031 56 -00003 Re 15 -00096 5T 00002 a 16 .00098 58 -00000 Ae 17 -00045 59 -0.00000 S24 18 0.00022 60 0.00000 BS 19 -00064 61 -00002 =. 4 20 -00067 62 -00C02 a ed 21 -00041 63 .00002 : 22 -00012 64 -00001 es 23 -0.00002 65 -0.00000 ae ok 0.00005 66 -00001 aa 25 .00022 67 -00001 é -00034 68 -C0000 27 .00033 69 0.00000 of 28 -00020 70 0.00000 ceil 29 -00005 a 30 -0 .00005 Ae 31 .00005 32 0.00001 33 -O0007 34 -O0COT 35 .00002 = 36 -0.00005 : Sd -00010 ce 38 -00010 He 29 ; -00006 eee 40 -00002 Hae ak -0.00000 63 SOLUS earrapCBen EN ES aan nae Ue ad ae aD Yanea AOS Se 6 ieieew 4 NE Oe) heed: Balle’ ek FILTER NO. 31 - r= 0.03, hk = 0.055, MW = 30, F = 9.0008, OO ODNAMFWHWFO ad Tac = 0-145 Value of k Wy 0.16999 16 -16020 17 -13325_- 18 -09564 19 -05580 20 -02152 21 -0.00217 22 -01399 23 -01597 2k -01206 25 -00639 26 -00188 2T 0.00029 28 -00045 29 -0.00032 _ 30 -0.00097 FILTER NO. 32 - rp = 0.03,% = 0.055, SWMIAUMEWNHHO Tae 79-135 Value of k We 0.17007 11 -16027 12 -13333 13 09572 14 -05587 | ; 15 .02160 16 -0.00210 17 -01391 18 -01589 19 -01198 20 -0.00631 N= Value of 20, F = 0.0004, Value of Wy -0.00180 0.00036 .00052 0.00025 .00090 .00092 .00038 0.00029 .OCOTL 0.00073 FILTER NO. 33 - ro = 0.03, 2 = 0.055, V = 10,F = 0.009, ro, = 0-135 > k Value of Value of We M,. 0.16991 -16012 -13317 -0.00225 -O1407 -01605 SWS Nala eal aR FOehAE o: WM FWNrFO OO OA OO -09556 01214 t -05572 al -C.006"'7 ; 0.02144 é 2 ‘ i 65 REICH a Pond This Ravaras we bo meek 9 ihe ee YG quent gute et o5i'e % bxo.e™ * Be inh 66 FILTER NO. 34 -r, = 0.03, = 0.08, N= 60, F = 0.0000h, O ON AW FWNHi- CO = {o) Tac = 0.205 Valve of W., 0.22000 . 19808 -14188 LO7TLAT -01954 -0.01020 -01654 -O1044 -00313 -GO004 -00063 -00179 -00169 .00062 0.00022 -00024 -0.00015 -00030 -00C06 0.00025 -00031 -00014 -0.00001 0.00003 -09015 -06020 -000L2 -00002 -0.00000 0.00005 -00009 .000C6 -0.00001 -00004 -00002 ©.00002 .Q0001 -0.00003 -00005 -00004 -00001 -0.00000 ea | i na a a RC Nm ee im MERAY AT PD | A. k Value of Wi he -0.90002 43 00004 hy .06003 45 -O0001 h6 0.00000 U7 -0.00000 48 .C0002 Fie) .000C2 50 0.00009 51 -OCOO01 52 -O000L 53 - 20000 54 -0.00000 » 0.00000 5 -00002 ST .00002 58 - 00001 59 ; . 00000 30 0.00000 ANS Py peta AEN Ses 3 PORT ee OR i 9 beaint rd Coeiite we wea sheen lk be a athe am ei Ow 40 - ke 1 Om OS am ing 4 ra x os 4 ert «See ENG x seh, May SS a ss ne ee fons pee os wiay canal ier ase CO) , her igh ’ *: AOKI 29 ee aS: 3 My i 7 ibs b ; 4 he i api ra f Has as 5 G + > oh Ae id er thee we: : . er r FILTER NO. 35 - re = 0.03, 2 = 0.08, N Foo = 0-185 Value of k Wy 0.2)799 16 1983 17 L123 18 O74 +6 19 .01G53 a -0.01021 al 01655 22 01045 23 -00313 ek -00006 25 -90063 26 00180 eT 00170 28 .00062 29 0.00021 30 0.00024 a ec cra Nea B = 30, F = 0.0004, Value of SP ee a ht eee [o} {S) 8 =~] eae iy Mary Stil ona FILTER NO. 36 - ro= 0.03, 2 = 0.08, M= 20,F = 0.001, k [o) COON AuUFWNHEH = Tes 0,185 Value of k Wy C .22003 oh) .19812 12 14192 13 07450 14 01957 15 -2.01017 16 01651 1T 01041 18 00310 19 -00003 20 -0.00060 em RE me eect Value of Wy -0.00176 -00166 -00059 0.00025 -00027 -0.00012 .00027 .00003 0.00028 0.00034 67 ae ee RR I NA Typed terse Atanen oo é me. we 1 ew a) aay Sapam!) eat ean? ‘hp : A) : 3. 9 ‘ey gM of) # Satie sheer ‘eee a _ atl ae: 5 ace = get hae ss ay B ae Ye een he: of | aa ye Oe = a eno E re Ss ideianaelietmauie® 5 te ager y a SRESEL TLE. FILTER NO. r, = Tac = 0.08, » = 0.195 k Value of UFWHEO ° as a (eo) 0.08, N Oro O-7 OV 10, F=0 Value of -0.90091 O07; Pes ee cohen lg a + wiht on a ve, sealasiaaid men 7 + ca - = h toad isa: heeatiye sss el Ae ee eee eee ee ee ee pacers ui etd Rind NALA ORET ER AEE SRR 4 FILTER NO. 38 - ry = 0.03,h = 0.1, WM = 60, # = 0.00005, ri = 0-225 k Vaiue of k Value of ¢ Wy. W, (0) 0.26000 he -0.00000 F 1 22348 43 -00000 2 -13635 4h .00002 g 3 04750 45 -00002 : 4 -0.00517 46 .00000 H 5 -O1717 U7 0.00000 H 6 .00886 48 -0.00001 é 7 .00110 meg .00001 ; 8 -00033 50 .00000 i 9 -00210 51 0.00001 : 10 .00202 52 .00000 : nak .00054 53 -0.00000 : 12 0.00014 54 0.00000 : 13 -0.00027 55 .00001 : 14 -00055 56 -00001 15 .00019 57 .00000 ; 16 0.00019 58 -00000 ‘ LY -00012 59 - .C0001 : 18 -0.00009 60 -00001 19 .00004 20 0.00015 j 21 .00017 1 22 . C0004 : 23 -0.00000 ; eu 0.00008 i 25 0.90013 26 .00006 27 -0.00000 28 0.00002 ego. C«; . 00007 30 -00004 31 -0.00001 32 .00002 33 0.00002 3h .00002 35 -0.00002 36 -00003 37 .00001 38 0.00000 39 -0.00001 ho .00003 ky -0.00002 warlarlaseeccnasec " jqetieas nen mamaria ea en oy Meare fe i OT ATE TS SRE NW PEP aR re NRA IOSD i i 4 ar oe ; iy ve q ; oy : ‘ if. | ieee ae “ 1S tuap Ai) eae Oi iete crore ams teas meth free me, Ee iid “it i a i . : 5 at a, 1 ie oa ae ha = | | be a Ape von so aheshneeachibe a cee lena 0 eb Fa a Narn emi 5 ; 4 i ; ? F it i 3 i : i ne P Fake pe o ce 3 % Ry ot ie ae ee oo 1 7 3), i 7 a ahs 1 7 : to) oO Mg BNO 8) ROE gS 2 ee ene as Te, rs Pe ed ee ee RE nae SEAS OR 0 erat ash: veneer et rs ne me le Pe ma oe OTS SE. FILTER NO. 39 - ro = 0.03, k = 0.1, M = 30, F = 0.0003, r= 0.235 k Value of k Value of Wy Wy (e) 0.26000 16 0.00019 a - 22348 17 -00012 2 -13634 18 -0.C0010 3 -O4750 19 -00005 k -0.00518 20 0.00014 5 -O1717 21 -Q0017 6 -00886 2 -00004 T .00110 23 -0.00001 8 -00033 e4 0.00008 9 -00210 25 -00012 10 -00202 26 -00006 11 -00055 2T -0.00001 12 0.00013 28 0.00002 13 -0.00027 29 -00006 14 -00055 30 0.00004 15 -0.00019 FILTER NO. 40 - ro = 0.03, h = 0.1, MW = 20, F = 0.001, Tac = 0-225 k Value of k Value of Wy Wy (0) 0.26002 11 -0.00052 1 . 22350 12 0.00016 2 -13637 13 -0.00025 3 -O4752 14 -00052 k -0.00515 15 -00016 5 .01714 16 0.00022 6 -00883 17 -Q0015 7 -00108 18 -0.00007 8 -00031 39 -00002 9 -00207 20 0.00017 10 -0.00199 7O 4 Jeena 8 a se» th 7 2 ¥ ae. iret ; ee eer RS . : Dies. : a he £ 9 TIO. ae aoa 208 ea a | re wn ies i ts con 98 P ‘ BY | ‘i { ; - Th en ‘ Da ag oti A neeminariaee Pe os Ty FILTER NO. 49 - Tes 0.05, k = 0.03, N = 90, F = 0.90009, Fae = Os1d5 k Value of k Value of k Value of Wy Wy et 0) 0.16000 42 0.00002 8h -0.00004 j 2), -15283 43 .00003 5 -00003 2 13258 4h -0.00001 86 .00002 i 3 .10272 4S .00009 87 .00001 : k .06820 46 -00015 88 0.00000 5 03437 U7 .00018 89 .OCGOO1 6 .00588 48 -00016 30 0.00001 ; T -0.01414 Fie) .00009 : 8 02455 50 0.00006 9 02617 51 00008 10 02126 52 00013 ! 11 01285 53 00013 12 00392 5k 00010 13 0.00327 55 00005 14 -00748 56 -00001 15 .00857 57 -0.00001 16 00722 58 00000 17 00455 59 0.00001 18 00172 60 00003 19 -0.00045 61 - 00003 20 00159 62 .00002 al -00175 63 -0.00002 22 00130 64 00005 23 00065 65 00007 a4 00016 66 06008 25 0.00000 67 00006 26 -0.00013 68 00002 2 00039 69 0.00001 Ais) 00059 TO .00003 29 00061 val 00004 30 ooo0k2 72 00003 31 00009 73 00002 32 0.00026 74 00000 33 00051 15 00000 34 06058 76 00000 35 00050 17 00002 36 00030 78 00003 37 .00009 79 00003 38 -0.00007 80 .00002 39 00013 81 00000 -00011 &2 -0.00001 ra -0.00004 83 -00003 TT ts ent nie : raat nna ae ee a om it q Sie, ee: Bre ay) ner Ger ie 1s 4 +7 oP ee ( i f ebodtadem: i ot <6 Oo 8 209 t+ Oe ee ae mae ve rh EE am bie ea ns ei ne , ; YP ALS iP a ' , 6 pe! Dea se a Sees as ey jae ae eR te bun oa een 9) ey) ae cee men =a Pee eee oe We pies FILTER NO. 51 - r, = 0.05, & FILTER NO. 52. r, s WMAKDUFEWHEKO k CU MDAAUFWHEO | cond roa 0.15 Value of .00593 -0.01409 02450 02612 .02121 -01280 9.03, N = 30, F = 0.0C4, = 0.05, he= 0.03, N= Value of Vy Q.00727 -CO460 -OULTT -0.00040 -00154 -00170 -00125 . 00060 -00011 0.00005 -0.00008 -00034 -00054 .00056 -0.00037 20, F = 0.01, eh On105 Value of k Value of W;. W, 0.15978 il -0.01307 15201 12 004,13 -13236 13 0.00306 .10250 ai ‘oore es 15 00835 03415 16 ‘00700 -00566 17 .004 34 -0.01436 18 "00150 -O24TT 19 -0.00067 -0.02148 z : i % | - 3 i 4 4 pie wenere To ODP CBSE ESTELLE BH eee OTD Qa Ace Lata ae ast ‘RU rie asses eames II Ook o> Naas AT Sn fm Go tele Bs eae a Dy. gai -ea alae C2 Aare wes OF 5p teat te _ FILTER NO, 53 - r, = 0.05, 4 =.0:05, N= 70, £= 0.00008, nee O.145 k Value of k Value ot W Wy (0) 0.20000 ko -0.00008 n . 18536 43 - C0006 2 ~14578 44 .00002 3 -09268 45 0.00000 L O4015 46 -0.00001 5 - 00000 L7 . 00004 6 -0.02190 48 -00006 T -O2648 49 -OCCO4 8 -01962 50 0.0CG000 9 -00833 51 -00003 10 0.00000 52 -O00004 ll .OO421 53 -00003 12 00429 54 -OOCOL 13 -00238 55 . 00000 14 . 00060 50 -00001 15 -OGUU0 ST -Cv002 16 .00039 58 - 00003 17 .00099 59 -00002 18 -00114 60 -0CO0O 19 .09070 61 -~0.00001 20 . 00000 62 -00002 al -0.00051 63 -00002 22 -00061 64 . 09000 23 .00038 65 0.00000 ck 00011 66 -0.00000 25 0.00000 67 -QOCO1 26 -0.00008 08 -00002 a -00023 69 .00001 28 .00029 7O O.00000 29 .00019 30 0.00000 31 -00015 32 : .00019 33 -00013 34 -OG004 35 -OG000 30 - 00003 3 -GO009 33 -00011 29 .00008 i) 00000 hl -0.00006 meee resem ae ae At eon Te ee eee i Be ee ee ee ee ; as 6S ee os a9 an) eh RR a oY Sn oe an ‘ ae te) + > Spee eeeseeeee LB -— oe ett Eee S pEoeteasne “SEersseseesr= FILTER NO. 54 - ro = 0.05, h = 0.05, WO ONKHAY FWWFO Tag = 0-145 Value of k M. 0.19999 al - 13535 22 -14578 23 -09267 ah -O4014 25 -0.00001 26 -02191 27 -02648 28 -01963 29 -00883 30 -00001 31 0.00421 32 -00426 33 -00237 34 - 00060 35 -0.0000i . 36 0.00038 37 .00098 38 .00113 39 -00069 ho -0.00001 ow ir LT PLIES. = lo, F= 0.0006, Value of La -0.00052 .00061 -00039 -00012 .00001 .00009 -00024 .00029 .00019 .00001 0.50015 .c0018 -00012 -00003 =0.00001 0.00003 -00008 -00011 -0C007 -0.00001 N i : i Por none eta hse ttings Monin NRE eee ee ene etn Peer ae te 81 a eee ees serena irneapenreennnaredienemeneen ROU a“ 2 Val Cv eas TNS As ie — eA. | ae ‘ i ; f r : ; , : i ee - * h ee Ree, Osan as me ee ih BO. im Pe if CALND ae sR ieee J a 4 wre tree Ss BREE ee ens a SKLBKSEL al = 2 oo Ah s fee Elissa ccastiseee Ri I a ae ee : Aseze FILTER NO. WOONAW FWWrO FILTER NO. OW OAADAWFWHrHO = 82 99 - 7, = 0.05, h = 0.05, N = 30, F = 0.001, Tac = 0-145 Value of k Value of Wy Wy Q.20002 16 0.00041 18537 17 .00101 14580 18 .00116 09270 19 .00072 OL017 20 .0C002 .00002 2 -0.00049 -0.92188 22 .00059 02646 23 .00036 -01961 oh .00009 ~ ,00881 25 0.00002 0.00002 26 -0.00007 .00423 27 -00022 -00431 28 .0C027 .00°39 29 .00017 .00062 30 0.00002 0.00002 56 - ro = 0.05, 2 = 0.05, W = 20, E = 0.00h, Tae = 0-145 Value of k Value of Wy Wy. 0.19991 11 0.00412 -18526 ; 12 -00420 14569 13 .00229 -09259 14 .00051 -O4006 15 -0.00009 -0.00009 16 0.00030 -02199 17 .00090 -02657 18 -00105 .O1971 19 -00061 .00892 20 -0.00009 -0.00009 ag ed dre : TE OE TS OCT TRE ae Satie Pcranep aye : ¥ - - . . io rs ey A r ” a 4 - ~~ ae ey manana st clei inrw coogi ee rt pace fag Sor 20 nae a8 ea ae = bay! SOR Mp oy aes me ier: inte om i ‘y Bt aah . ee , aaah <<) Re ae > Sos coche ee ae ee = _@nRRrgemsensrere | > Ee oa eet cs ere aye od Ace 6b ie. Bite ipeeete +39 FILTER NO. 57 - rg = 0.05, h = 0.08, N = 60, £ = 0.00009, WONDUFWNHFE O nei 0.205 Value of k Value of W hy. 0.26006 ho 0.00001 -22653 43 -0.000292 -14416 4h 00004 -O5417 4S .00002 -0.00665 46 .00000 -02671 UT - 00000 -01925 48 -00002 -00564 kg -00002 0.00114 50 -00000 -00080 51 0.00002 -0.00101 52 -O0001 -00079 53 .00000 0.00069 54 .00000 .C0135 55 00001 .0007T9 56 -00002 .00009 ST .00001 .00007 58 -0.00000 .00040 59 - 00000 -00043 60 0.00000 .00009 -0.00019 -00014 0.00001 -00001 -0.00014 .00020 .00011 0.00000 .00001 -0.00006 00006 0.00002 00008 00005 Q0001 .O0001L .00004 -00006 .00002 -0.00002 -00002 0.00001 83 jf i j i ee ee at ae ee et ae] 7 ae hc Asa FS MR oe . ai i ‘ee » f is ‘a cd Ri og iN ‘ 7 z ’ el ; = ee pe Tee i 1" | & i Ae rer i 7 Ae a. UN, & : ae ¥ . SO. ; ' 5500, re ‘ AGORA tw ; Rs aoe : RoR i i ‘a5 L A. Ta, ae KY. ? PMR eee Lee ty J. oe eae Lee j I . i 4 4 é t we } | A ° 7. } | le eee n IE are a FILTER NO. 58 - ro = 0.05, h = 0.08, MW = 30,F = 0.0005, a = CRS k Value of k Value of Wy Wy, fe) 0.26001 16 0.00008 1 -22654 17 00041 2 ~ 14416 18 00044 3 -05417 19 .00009 4 -0.00664 20 -0.00018 5 .02670 al 00014 6 .01924 22 0.00002 7 -00563 23 00002 8 0.00114 24 -0.00013 9 .00080 25 00020 10 -0.00101 26 -00010 11 00078 27 0.00001 12 0.00070 28 -00001 13 -00136 29 -0.00005 14 .00079 30 00005 15 -00010 FILTER NO. 59 - rz = 0.05, h = 0.08, N= 20, F = 0.001, aya 0.205 k Value of k Value of W,, W,. ) 0.25998 11 -0.00081 iv 22651 12 0.00066 2 Lakh 13 -00133 3 -05414 14 -00076 4 -0.00668 15 . 00007 5 -02673 16 -00005 6 -01927 17 -00038 7 -00566 18 -O0041 8 0.00111 19 - 00006 9 -O0077 20 -0.00021 10 -0.00104 ne ena “Ta We pan eters com sepia ee . F ey , a I ‘he ie 4 Wh jl f a ; ONT Croton ae 1 sivas i i eee tte hese a ee ; ee 1 a i ; ‘ ; ‘ ¥ Mia a ’ ’ : whe Se = * Boy uecie sit a ‘a - ée 8 tate epee": Pee « i “se a ; er lt tes las. 4 Sa Fed 17a ed. a Tah Li Pig ue, ae te ae fi | ee RON wit I tt ae . a a Rh = : Ge KT (BE ts 2 a NE . ABO, ¥ nt ; | aa ° Sek ae Sets. ee RAITT IE eee eR ea ot nyt ne te ne a 4 Bale a UE pack Ce ok NS SNL ain UA an NLR eR NUMER NYC ERRNO art Ta FILTER NO. 60 - r > = 0.05, hk = 0.08, VM = 10, £ = 0.007, ne 0.215 k Value of k Value of W W. k a ) 0.26023 6 -0.01901 1 -22677 T -00540 2 - 14439 8 0.00137 3 -O5440 9 -00103 y -0.00642 10 -0.00078 5 .02648 FILTER NO. 61 - 7 = 0.05, % = 0.1, V = 50, F = 0.00008, ‘ 2 3 i ! | i i | } | { | Pe 0.245 k Value of k Value of W Wy O 0.30000 26 -0.00005 1 - 24802 27 0.00001 2 - 12993 28 -0.00003 3 -02303 29 00005 \ 4 -0.02426 30 0.00000 5 .02122 31 -00004 6 -00530 32 00002 ! 7 0.00064 33 -0.00000 8 -0.00126 34 0.00002 | 9 .00193 35 .00005 10 0.00000 36 .00002 11 -00103 37 - 00000 | 12 -00035 38 -O0001 13 -0.00609 39 -0Q002 14 0.00036 Ye) - 00000 i -00061 hi -0.00002 16 00024 4o -00001 17 -0.00004 43 0.00000 18 0.00010 hy -0.00001 19 00019 ks 00002 20 00000 46 00001 el -0.00014 47 0.00000 22 00006 48 -0.00000 23 0.00002 Ke) 00001 ok -0.00007 50 0.Q0000 25 -0.00013 85 Sepsen Sse are) Waietre teeter - mead * bt Pe eae “- Hi: a ae 2 ; au hoe tps iW Asi a % Laken ie lay ss Gantsen: a ike f Brea ROSE P op an nh ENT BT CEES RE FILTER NO. 62 - re = 0.05, h = 0.1, M = 30,£ = 0.0003, Tac = 0-245 k Value of k Value of Wy, Wi, (e) 0.30000 15 0.00024 BL 24803 lf -0.00004 2 - 12993 18 0.00011 3 .02303 19 .20020 4 -0.02425 20 - 00000 5 .02122 21 -0.00014 6 -00530 22 -00005 7 0.00064 23 0.00002 8 -0.00126 24 -0.00006 9 .00193 25 .00012 10 0.00000 26 .00005 sit -9010% 27 0.G0001 12 ,00036 28 -0.00002 13 -0.00009 29 -00005 14 0.00036 30 0.00000 5 0.00061 FILTER NO. 63 - rg = 0.05,h = 0.1, N= 20, EF = 0.001, Tac = 0.2k5 k Value of k Value of W,, W 0) 0.29998 11 0.00101 1 - 24800 12 -00034 2 -12991 13 -9.00011 3 .02301 iy 0.00034 4 -0.02428 15 -00059 5 02124 16. - -00022 - 6 -00532 17 -0.00006 7 0.00062 18 0.00008 8 -0.00128 19 -CQU1T 9 .00195 20 -0.00002 10 .00G02 Sy op Pepe ae oer | Pi & ae sek, : oe en My ; Ue e eo) ane a bates’ om . - pant tia beh iran eH haa iy eri och Tha aie, ean a BE mI Ea de ’ A 7 ae Ee ct '¥ iy { Me | ie % A Y it ew! eaetrate fm Ar ees Bol: eo Laey - hy Wa ; He a pA ah eh 4 ae tgs bs 7] ee ee Oo eM ky i allay ‘- OS ea iets 2 LD He: CRIA DET IAS NOR ER HN NRC SL I RL aS RR SR A EN ne FILTER 20. 64 - ro = 0.05, r = 0.1, N= 10, = Tac = 0-245 kK. Value of k Value of Ww, Wy, ) 0.30023 6 -0.00507 1 -2hS2k 7 0.00086 - 2 - 13015 8 -0.00104 3 -02325 9 -OO1T72 4 -0.02403 10 0.09023 5 -0.02100 ‘ 4 | i ' ‘ 4 j i | lie >in ERS LS .e@ 87 vd y -W, t: ny 3 if * Ses ea RA 1 5 he oP 71 ate * Nee Ke ye ESI ant ohathiech tein FILTER NO. 65 - r,= 0.05, h = 0.2, W = 70, B = 0.000007, | Yac= C.445 k Value of k Value of Wy, W,, | ) 0.50000 42 0.00000 a 27323 43 -0.00000 ; | 2 .00000 4h 0.00000 3 -0.01803 45 -0.00000 4 0.00009 - 46 0.00000 5 -0.00424 47 -0.00000 ‘ 6 0.00000 48 0.0000C | T -0.00121 kg -0.00000 8 0.00000 50 0.00000 9 -0.00021 51 -00000 | 10 0.00000 52 -00000 | 11 00012 53 .00000 12 0.00000 54 .00000 13 00018 55 -00000 14 .000U0 56 00000 15 00015 5 .00000 16 -00000 58 00000 ily? 00008 59 .00000 18 00000 60 .00000 19 00002 64 -0.00000 20 00000 62 0.00000 21 -0.00002 63 -0.00000 | 22 0.00000 64 0.00000 ( 23 -0.00003 65 -0.00000 alk 0.00000 66 0.00000 j 25 -0.00003 67 -0.00000 1 26 © .00000 68 0.00000 | 27 -0.00002 69 -0.c0000 28 0.00000 70 0.00000 i 29 =0.00001 : 30 0.00000 \ 31 .00000 32 .00000 | 33 .00001 34 700000 35 .00001 | 36 -00000 i 37 .00001 38 .00000 39 .00000 4O .00000 ki -0.00000 j : : i et RR A LE | A 7 % EY d Utbaty gra bay a | F % - Yr i ¢ by | ; Eat rs esi hey F Ih a an “A p i \ ORISA 7S ‘OE ” 4 VOGT. O 4 i ; « CHAGOO 1 CR iia Os a Cree Jy: pee aes x oe aC 5 ha RD BORK, t ‘ ROO,” , OOOG., wes On. HOOK, 9 og ee La al i 12: it 1 2% bi ise ‘ : ) i = - Po i i 2 ; > ¥ pup bs ae, Veg vm ’ ba! Bens 4 v-cbit eae yienanelanaeana 7 +08 BODO a ai con ~ % ees sae 48 oe ie —e aes a> % 7 & ln é ra ~ ty fa ae rt: SESau a ihe f 2, ni) Ra nn Oats ‘~ $SL00. Ce i ue RORY : PE PFU PIS A ie re, a Me sie eee Jay 7 at ' a ; we = ? Sn een’ 5 os precdien 7 “ enpikeere ie xe ~ B am te it a a : et FILTER NO. 66 - r, = 0.05, h= 0.2, = 30,£= 0.00007, Ts = O.445 k Value of ° ° Wy O Q.50000 1 227323 2 -00000 3 -0.01203 4 0.Q0000 5 -0.00424 6 0.00000 T -0.00121 8 0.00000 _ 9 -0.00021 10 0.00000 11 -00012 12 -00000 13 -00019 14 -00000 15 -OO0015 Value of We 0.00000 .00008 - 00000 -00002 -O00000 -0.00002 0.00000 -0.00003 0.00000 -0.00003 0.00000 -0.00C02 0.00000 -0.00000 0.00000 FILTER NO. 67 - r, = 0.05, hk = 0.2, N= 20, EF = 0.0002, Tac = 0-445 k Value of OO OADM FWWMWrEO - ine) ie) -0.00000 — adore Value of -0.00000 0.00018 -0.00000 0.00014 -0.00000 0.00008 -0.00000 0.00002 -0.0C000 ae f et ABO EPEAT EDA BEL : ne ae a en PR LR ES 4 f i 3 | 3 iA f 4 pO eee we eae. a oe ae ae i fy ya. Sip eer ver GHA ws Ke -, CRD AYR ay). pe BPC: Cerner a wr #090 : COOH oy {jn a Ce eg ihe WOOKO.8 OoeeaBe RES aR « EV Boeke Aral ” rend ie i. Sap wag Cie tree its we 1 FILTER NO. €8 -r = 0.05, = 0.2, N= 10, F = 0.001, Tac = 9 AUS k Value of k Value of W ie W k ie) 0.50004 6 0.00004 1 - 27326 7 -0.00i117 2 -O0004 8 0.00004 3 -0.01799 9 -0.00017 4 0.00004 10 0.00004 5 -0.00429 FILTER NO. 69 - r, = 0.05, = 0.2,N = 4, F = 0.01, Tac = 0-455 k Value of k Value of Wy W,, (e) 0.49884 2 -0.01919 al -27208 4 -G.00116 2 -0.00116 ig THERE, seen ete Mae =e ~ $ret Waihe a : vem i i By bea phar eer ‘FILTER NO. 70 - rz = 0.08 = 0 WON OWFWNHPE Oo 0.03, N = LO, E = 0.0004, Value of W,. gL en ae rae etn eeu oan ae ae i M q i 4 ; : | y »~ ee #3005 (Be TOME, Bsagh.- grea RS Ware 7 ae es Ie LOS SU CAR ie rr > a HACER, pe th fer: Bia ‘PaO, Scie, i reseed a >. em FILTER NO. 71 - 7, = 0.08, A = 0.03, W 2 30, F = 0.003, Tac = 0-135 k Value of k Value of Wy Ww oO 0.22002 16 -O.00731 l - 20224 17 C0429 2 -15426 18 -00056 3 .o9022 19 6.00196 4 02777 20 -00260 5 -0.01804 21 -C0183 6 -03958 22 .00065 T -03809 22 -@.00012 8 -02179 24 00024 fe) -00165 25 0.00002 10 0.01316 26 -00022 ll -01821 aT -O0O011 xe -O1427 28 -0.00026 13 -00563 29 -00061 14 -0.00270 30 -0.00066 a5 -00727 i FILTER NO. 72 - ro= 0.08, hk = 0.03, ¥ = 20, EF = 0.009, Je Tae= 0-135 k Value of k Value of W, Ww a k (0) 0.22007 ll 0.01826 1 - 20228 12 -01432 2 ~ 15431 13 -00567 3 09026 14 -0.00265 4 -02782 15 -00722 5 -0.01800 16 -00726 6 -03953 17 00424 7 -03804 18 .00052 8 .02174 19 0.00200 9 -00160 20 0.00264 10 0.01321 Fag RINE) PST SR sae et , don) he ey ‘ ¥ =e5 oy rN aioe es Oe ae Cee os en ed fe ee) ae To a { } 7 4% de Se © SER hs RE ee : ae idee Be eee s a 2 8 eel MO 8 SS a i P< a ‘ e MEMR FE "3 i ER Sh RRA Ee, eof oe a) VA Ge Pers a a pee 9 he a et FILTER NO. WcA OW FWhHFE OO (3 -0.04u89 -0.00070 -0.CO000 -0. Q. -O. 60, B = 0.00004, Value of 93 oo mar net eaten a a fen A nk NS ENR ARC URS A REAL cba Ai oS TO, A 3 : RT re er ee er Rear a oto” gk ps Pi aS Oey ae » eae, son vey h Aud oy tn chit SA be. Ey f tase _— ake tt hoe = Brie peer, =e OOOO SHO ath mee: GOK afoes. SKK: at aaaete a AG Hs FILTER NO. 74 - WO ONIKNUFUNFHO FILTER NO. 75 - C\10O OA ADAM FWH+t- O = ro = 0.08, h = 0.08, N= 30, £ = 0.0004, Pac = 0-235 Value of k Vaiue of 0.32000 16 -0.00005 - 26239 LT -00041 - 13070 18 -00035 -01065 19 0.00012 -0.04089 20 -00031 : 4 .031.40 al .00012 -00487 22 -00001 { 0.00721 23 00013 ( 00449 2k 00017 00034 25 00000 f 00063 26 -0.00013 00185 2T 00007 .00090 28 Q.00000 -0.00070 29 -0.00004 -00086 30 -0.00009 -0.00017 re = 0.08, k= 0.08, N = 20, F = 0.001, Tac = 0-235 Value of k Value of Wy. ~ = Wy ri af 0.32001 zi 0.00186 26239 12 00091 13070 13 -0.00069 01066 14 00086 -0.04089 15 00017 03139 ~ 16 00005 00486 17 00040 9.00721 18 00034 00449 19 0.00012 00034 20 0.00031 00063 ‘ Spe aenst ee SA ese DS? Scns on g reS CS tess MR ate Ps eo * aseusasnacereee ¢ = 5 = ee eee eS eR ONS a: ee | a7. Esra Ebi = 3 aa ee 0 oe ik ein == >> -= ee F ae ees is Ut RS Ronee seo ee a FILTER NO. 76 - "c= 0-08, h = 0.08, N= 10, F = 0.0006, rae = 0-245 k Value of k Value of Wy Wy 6 -0.00480 » 26246 7 0.00728 8 -00456 00042 0.00070 ‘ WwW Fwhor oOo eee = (e} “4 WwW ow Arnon anes SUCRE Be gh ERE a De Pt Late Le I 81 Spee Ea RSS SA et os 99 a Ate is rab a ers homes Pl ret | ‘ 96. FILTER NO. WOON NU FWhHrFEO TT - ro = 0.08, h = 0.1, MW = 50, F = 0.00008, rac= 0-215 Value of 0.00003 -00002 -0.00001 0.00003 -00004 - 00000 -0.00001 0.00001 -0.00000 -00003 -0.00002 k Value of Wie \ ho 0.00000 | 43 -0.00001 yy -Q0001 \ 5S 0.00001 6 -00002 U7 -O00000 48 -00000 4g -OO001 a A kt alain AS Ope kiet ar aN i siti) ie SSS SE FILTER NO. 78 - ro = 0.08,h = 0.1, W = 30, F = 0.0002, Tag = 0-285 k Value of x Value of Lie oie (e) 0.26000 16 -0.00027 1 -2T THO NG 0.00065 2 -10527 18 -0.00019 3 -0.01853 19 -COO11L i 0405) 20 0.00015 | 5 .01247 tt 21 -00018 6 0.00435 22 -Q0002 T 00205 23 o0004 8 -0.00048 ok 00011 9 0.00164 25 00000 10 00202 26 -0.00008 11 00016 2T 00002 12 -0.00031 28 - 00000 13 0.00025 29 -00006 14 -0.00007 30 -00004 15 -0.00057 FILTER NO. 79 - r, = 0.08, h = 0.1, W = 20, F = 0.0008, Tac = 0-275 k Value of k Value of Wy Wy o) 0.36001 11 O.00017 at -2T7740 12 -0.00030 2 - 10527 13 0.00025 3 -0.01852 14 -0.00007 k -04053 15 . 00057 5 -01246 16 -00027 6 0.00435 17 0.00006 - 16 ~ 00206 18 -0.00010 i 8 -0.00048 19 -00011 | Q 0.00165 20 0.00016 10 0.00203 a np aoa COU Poe 9T i Oat Het aa ‘ i a a 4 : my a = eg eo 2.0 8 OEM he Ray 30 wie ®® Stray rar as ~~ : ARS. See & ed 6] RY 4 a GOL Ga6t0..0-' a hu ee fam «ft W000 % 1 othe Pi eros UE VOM ke REG. ae Oh wr TOO, ‘ ™ OK, iy LOO. ¢ BLIND ' LG > AICO bb0. + gy 5B vn Pas a as BG, » — 3 eS me & is EAT RE ' ore ‘ ne ve * LOO 0 BRO. a wv om ee ete EE eRSs tf “7 tee Te a z! wa ca A , ee Vie Boos “9 wey Olt ASE, v9 > hake : FILTER NO. 80 - r, = 0.08, h = 9.1, ¥ = 10, F = 0.003, Tac= 0.275 ~ k Value of Kk Value of les ir fo) 0.35994 6 0.00428 1 »27733 T -00199 2 -10520 8 -0.60055 3 -0.01860 9 0.00157 4 -04060 10 0.00195 5 -0.01254 Ne At nee yw NOES AT ee rp Am em FILTER NO. 81 - r, = 0.08, A = 0.2, N = 70, F = 0.000007, a Tao= 0.475 2 k Value cf k Value of 4 Wy Wy 4 0 0.56000 ho -0.00000 : 1 26839 43 0.00000 2 -0.03038 lly -0.00000 : 3 01523 45 0.00000 , i .00182 46 .00000 fc 5 00250 47 - .00000 ; 6 0.00067 48 -00000 4 T -0.00030 4g -00000 4 8 0.00080 50 -00000 3 9 00003 51 -0.00000 3 10 -00048 52 -00000 ‘ He: -0.00006 53 -00000 ; 12 0.00018 5k -00C00 : 13 -0.00014 55 -00000 i 14 0.00003 56 0.00000 i 15 -0.00014 57 -0.00000 16 00000 58 0.00000 { 17 00008 59 -00000 4 18 0.00002 60 -00000 19 -0.00002 61 -0.00000 f 20 0.00004 62 0.00000 21 -00001 63 -0.00000 ‘ 22 00003 64 0.00000 H 23 -00001 65 -0.00000 2k 00001 66 -C0000 25 00000 67 -00000 26 -0.00001 68 0.00000 F 27 00001 69 -0.00000 28 00002 70 0.00000 29 00000 i 30 .00001 : 31 0.00000 32 -0.00000 33 0.00001 34 00000 35 -00001 36 -0.G0000 37 0.00001 38 -0.00001 39 0.00000 We) -0.00001 41 -0.00000 ; a ee rm ee cel NN RR RR le EN UCR iene: uauiapeare Sa SE OS FILTER NO. 82 - r.= 0.08, k = 0.2, N= 50, F = 0.00003, reget O4T5 } k Value of’. k Value of Wy Wie | t (e) 0.56000 ho -Q.00001 1 26839 5 43 0.00000 2 -0.03038 4h -0.00000 (iets 3 -01523 45 0.00000 y -00182 «6 -O00000 H 5 -00249 47 -00000 6 0.00067 48 -O00000 . 1 -0.00030 kg -00000 8 0.00040 50 -0.00000 9 .00003 10 -00048 i 11 -0.00006 12 0.00018 13 -0.00014 14 0.00003 15 -0.00014 16 -00000 17 .00008 18 0.00002 19 -0.00002 20 0.00004 a1 -00001 22 -00003 i 23 -00001 ek .00001 25 -0.00000 26 .00001 2T -00001 28 .00002 29 .00000 30 -00001 31 0.00000 32 -0.00000 33 0.00001 3h -000C0 35 .00001 36 -0.00000 37 0.00001 38 -0.00001 39 0.00000 -0.00001 Wi -0.00000 100 H Garp ei al te Fe ey Wane 1 op Som Sheen pn pas ey os Iw a 408) nf hes bie Piva” 56) ra be aXe 4 Aaalanis * i a va F “Roses 2) TE eas Dest rae SCORED. FOC * pala > ey ax NESS, SS) a EL A ae ee se ath St ees | nee, | ! | | | | | | | | | | | Seago aero eee FILTER NO. 83 - ro = 0.08, hk = 0.2, W = 20,F = 0.0002, FWNrF OC OW ON OW bh FILTER NO. 84 - UM FWNRO FILTER NO. 85 - k Nyro Tac = O-LT5 Value of k Value of Wy Wy 0.56000 11 -0.00006 - 26839 12 0.0001 -0.03038 1S} -0.00014 -01522 14 0.00002 -00182 15 -0.00014 00249 16 .GOC00 0.00068 17 .00008 =0.00030 18 0.00002 0.00061 19 -0.00002 -00003 20 0.00004 0.00048 r, = 0.08, k = 0.2, N= 10, £ = 0.001, Tac= 0-485 Value of k Value of vy W, 0.55999 6 0.00066 - 26838 7 -0.00032 -0.03040 8 0.GO0079 -01524 9 -O0001 00184 10 0.00047 -0.00251 i ro = 0.08, h = 0.2,N = 4, FE = 0.01, Tea 0.465 Value of a k Value of Wi W, 0.50074 3 -0.07101 - 30600 L 0.03707 -0.05243 i 101 Bie pies Boat aki nn RR ESN IEE OE DRL 5 TC TTT sono. > a! a 78 wun te¥ ‘ hg Oe oR Oe ¥ Ca . TTR Rg ae a ere FILTER NO. 86 - r si WO OBANAYFWHEO 102 ~y a ar ee 0.26000 -23126 -15671 -06561 -0.00945 .04730 .O4607 -02058 0.00792 -02334 -02126 -00799 -0.00580 .01224 .00989 .06278 0.190354 -00572 -00394 .00068 -0.00159 -00192 -00100 -00005 0.00023 -0.00000 -00018 0.00003 -O0046 -00067 00042 -0.00014 -00059 .00064 -00029 0.00016 - 00040 -90033 -00010 -0.00008 -O0011 -0.00004 = 0.1, h = 0.03, W = 60, F = 0.0006, i een re OER RIO AEC OE EE: Sond AS! ob eceHOnad PEER RON BE SR mS OM A aR wet) om en a, | ae & nt aaa SRO A EmV a me. 7 Aeon ve r d Len RRReeseeees RR ied F 7 + ROSE eRe a Be eae: , 3 < x > = a % Lead , 5 lll «a lal} Us fi ‘ Ay a Tord sa MRT tears ae oem tania whetenetrenn rt Nem tre he me FILTER NO. S57 - ry 2 0.1, 2 = 0.03, ¥ (Sa ee ad oo Wh M OW MANO hk oS us FILTER No. x oO i 3 2 ce) ¢ be S; 10 Mae & Ou165 Value of x a’ 0. 2599T 16 +o 3123 if 15668 18 £00558 19 0.00948 20 04733 eal 04610 22 02061 23 0.00789 ee 02331 25 £02123 Byars 00796 eT -0.00583 2 .OL22 2 .oog9g2 20 O0L82 Value of Wy 0.00351 -COS69 -CO391 -00005 -0.00162 -O0195 -O0103 -CCoo8 €.00020 -0.00003 -CCo02 -00000 0.00042 00064 0.00039 - re 2 0.1, h = 0.03, VN = 2, F = 0.009, ati 0.155 Value or x a» 0.25989 vat Areas uaa 12 - 15600 13 06549 14 VU .00950 15 O44 lo -O4018 , We sQ2069 18 0.00782 19 0252" poe) O.00115 Value of 00383 .00056 -0.0017¢ 103 oe fae rn tf ee neat wn a na RI a usd ik 88 RAY SPST 5: eS. Sakae okd

4! & i eon) Sates -e =, ee Lie Reis SOAR RP OIA, ana (eS ete z ie e- 44 Dares, fe. Pad oe Fee atten aye d, , - ee a ye et AAS, - 7 = ©. Free c 2 ZAG : ee ay y, ev A: 4 se sess 's sOcaes LSLLs 4 CO OHA f . OG Leo Z; S(2 9) Sed 6} “0.4L n VOLel z 000z2 ie HOLT 1h .O00%6 Ly -0.00000 FILTER NO. Gb = or ac k Value of : W, 6) : 0. 34054 ! Aras | 2 -OUOLK 5} -0.08 396 y O34 v ~=0.00U0L6 _cenpcenemnenareT RRR 4 Pees S zr se 5 RS y “a ‘a & ge ez ee i 4 6 0.cOCaZ iff -CCOS2 en COOOL “3 -00006 He) -0 .000c0 =~ 0.1, h= 0.1, = 10, £ = 0.005, Fag = 00295 k Value of Wy 6 0.00842 t .00105 3) -00062 y) -00212 10 -0.00016 107 epee a acne i eth AAO i Re TT UE LE 8 ES RE AN I FET ST TESS SORE Aw als en eamiaceny Uncen Naso : rar cae a mee an ERS aE el ae RS EC a ATE OR RE aE! BL ys HeEAd sue WSR SR RAE Sa ek os ae ya fbn sd 4 = ae eet ee a By 2 ee ee ie Ce ne ie we. as ee ee eR FILTER NO. 95 - rg = 0-1, h = 0.2, N= 70, FE = 0.000007, ac = 0-495 k Value of k Value of Wy W, ; © 0) 0.60000 ko -0.0G000 i a -25986 43 .O0000 ; 2 -0.04852 hy 00000 Doe 3 .01060 45 00000 | 4 -00253 46 0.00000 j 5 mrorourexa) 7 -O000CO0 6 0.00071 48 .Q0CO00 et 7 -00071 kg .00000 ~ 8 00047 50 . 00000 9 .00020 51 .0Q000 10 -0.90000 52 .00CV0 11 -00011 53 .00000 12 -00014 54 -Q0000 13 -00011 - 55 -00000 14 -00005 56 - 00000 15 . 00000 ST .00000 16 0.00004 58 - 00000 17 .00005 59 -00000 18 .00004 60 .CO0CO 19 .00002 61 . 00000 20 -0.00000 62 - 00000 21 .00002 63 -00000 22 -00002 64 .00COC 23 .00002 65 -0000U 2k .00001 66 .00000 25 -00000 67 .00000 26 0.00001 68 .00009 2T -00001 69 .00000 28 . 00001 TO 0.00000 29 .00001 30 -0.00000 31 .00000 2 -00001 33 .00001 34 .Q0000 35 ~ 00000 36 0.00000 37 .00000 38 -00000 i 39 -Q0000 : 4O -0.00000 Se -Q.00000 108 . ‘oe ootet Oe - aKa: Sl HOE, ~ SOGIRID SOg0u; ee aaa a tad itt REVECUER ES ~ 2 SES SEasnk ite FILTER NO. 96 - r, = 0.1,h = 0.2,M = 30, F = 0.00006, Tac = 0-495 k Value of k Value of Wy W, fe) 0.60000 -16 0.00004 1 ~ 25986 17 C0005 2 -0.04852 18 -CO00k 3 -01060 19 0c002 4 -00253 20 -O 00000 5 -00000 21 00002 6 0.00071 22 00002 7 .00072 23 00002 8 -00047 ek -00001 9 .00020 25 -00000 10 -0.C0000 26 O.GC001 11 00011 2T OOCOL Me 00014 28 00001 415 00011 29 -00001 14 -00005 : 30 -0.00000 15 -0.00006 FILTER NO. 97 - rg= 0.1, = 0.2, M = 20, £ = 0.002, Tag = 9-495 k Value of k Value of W, Wy Ce) 0.60000 11 -0.00011 1 -25986 12 00014 2 -0.04852 13 -OO0011 3 -02060 14 -00006 4 -00253 a5 -O0Q000 5 -00000 16 0.00003 6 0.00070 17 -00005 7 -00071 18 -COGO4 8 -00047 19 C0002 9 -00020 20 -0.00000 10 -0.00000 ie 109° PREG ee ATI AAS Apne arin near ae ae i 8 , ae | CS ¢: | ee i; a . * ee + ct.) ea ei ney. (6 CP agit an ahi rw } te BERR» fh acy AOR vit A ne bs 110 FILTER NO. 98 - re = O.1, A WM FWhNr Oo Tac = 0.499 Value of Wi 0.59997 -25983 -0.04854 01063 -00561 -0.00003 ~ ~ COO O- OV < | 100. = FILTER NO. 99 - r, = 0.2,h = 0.02, ¥ = GO, F=0.0006, i Ce gee a k Vulue of k Value of 4 0 0.46000 42 -0.00002 i st ~ 31474 43 -OCO05 ; 2 103905 Ey 0.00008 } 3 0.09573 45 -00012 ; mah .03641 46 -0.00008 { 5 0.04729 47 -00017 g 6 .03211 48 0.00005 ; T -0.02449 kg .00019 ‘ 8 .02691 50 -0.00000 bus) Pe OnOMie ge 52 -00017 t 10 02126 32 00004 i 710 -0.G0352 53 0.00012 ' 12 -O1572 54 .00005 { 13 .00063 55 -0.00006 . 14 0.01074 5 . 00004 15 .002738 5 0.00002 6: -0.00665 58 -90001 ny .OO21T 59 -00000 | 18 0.00360 oe) 0.00003 19 00262 } 20 -0.00159 oe 21 -OO1LTO : 22 0.00046 5 23 .00074 i 2h -0 .00004 i 25 .0000G i 26 0.00003 ! 2T ~0.00044 28 .000z2 - 29 0.00059 30 .0G042 31 -0.0G054 32 .00054 33 0 .CO035 34 .00054 35 -0.00016 30 90042 | 37 0.00002 38 00027 wos _ .00C0+ Lo -0.00011 hi -Q.00002 dil PRN HE la en RI A NR a a pe A LN A OEY