which can be tolerated. In table 1, r c = 0.3, h = 0.03, and 

 N = 20 will give the cutoff normalized frequency namely 

 r ac = 0.355. The absolute error E = 0.006 is seen to satisfy 

 the gain requirement. The corresponding f ac (the frequency 

 of the first zero crossing is (O.355)(8'0 = 29.8 cycles per 

 week. However the amplitude of the frequency components 

 between / c and f ac fall off rapidly in magnitude, the rate 

 of fall depending on the parameter h. 



The 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 c 

 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 cycles per week. The 

 calculated r c = 0.0357- The nearest value of r c in the table 

 is 0.03 which gives the cutoff frequency f c = 2.52 cycles per 

 week. If greater precision is desired, a set of weights may 

 be computed by equations (2l) through (2*+) using the appro- 

 priate r c to&eoner with the appropriate values of h and N. 



32 



