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APPENDIX: FILTER OATA 



Table 1 contains design parameters r c , h, r ac , E, and N. 

 Various filter parameter combinations are listed relative to 

 increasing values of r c in the following order 0.01, 0.03, 

 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 E increases . The filter number corresponds 

 to the arrangement of 118 sets of weights given in table 3. 



Table 2 gives the filter parameters r c , h, r arJ E, and N along 

 with the corresponding frequency-response data r and i?(r) 

 for filters numbered 1 to 4 inclusive. 



Table 3 gives the filter parameters r c , h, r ac , E, and .V and 

 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 components below 25 cycles per week 

 and rejecting higher frequency components. Also, there is 

 reason to believe that no frequency components exist in the 

 data higher than 0.5 f g . Then, f s = 0.5(12) (7) = h2 cycles 

 per week. 



1. Calculate r from the relation 



J i 

 and 



25 



O.298 



2. Select the value in table 1 nearest r' c . In the case 

 considered, r c = 0.3. Then / c - (Q.3J(34) = 25-2 cycles per 

 week, which is the ideal cutoff frequency f c for r c = 0.3. 



3- Finally select the smallest h (the sharpest cutoff) and 

 the smallest N consistent with the maximum error in the gain 



31 



