1. The phase shift must be identically zero for all 

 frequencies . 



2. (av+l) weights are to be used with S/ k = W-k. 



3- A filter gain of unity from zero frequency to the 

 ideal cutoff is required. 



k. The weight calculations are optimized in the least 

 square sense. 



5. The following corrections in the weights are mads 

 to further approximate the desired pre rer ties of the fre- 

 quency-response function. 



(a) The weights muse ue corrected to minimize the 

 oscillations beyond the first zero crossing of the fre- 

 quency -response function. This is done by terminatirg the 

 frequency response by means of a sine function characterized 

 by a parameter h. By selecting h sufficiently large, the 

 oscillations do not exceed the preselected limit. However 

 by increasing the value of h one decreases the shirpness of 

 the desired cutoff, since for h = the cutoff is sharp but 

 sharpness of cutoff decreases as h is made larger and larger. 



(b) A second correction is made in the weight 

 calculation to insure that the filter gain will be unity at 

 zero frequency. 



Formulas for calculating a set of weights, subject to 

 above conditions, and the corresponding frequency response 

 data are given by Marcel Martin. 4 The working formulas 

 for the necessary calculations follow: 



_ r C os(2gWi) ] I" sin2,ift (r e + ft) "1 , v 



Lh ~ [i-16 h? *?J I. *ft J K ' 



A= 1 - \z Q+ 2 J L k \ (22) 



ikx J 



X = 2 (r + h) (2j) 



i 



1 "^ 



i / 



17 



