NAPI TK-lij-ij-0 



Naturally, as the region of signal interest changes, so does the choice of 

 bandwidth; if the possible signal slopes lie between 3 - 5^5 (between -9 

 and -15 db/oct), the bandwidtli resulting in the smallest worst case loss 

 would be n, <%» O.U3. For the range of signal slopes plotted, the loss oA^er 

 and beyond the bandwidth loss of Figure h amounts to some 1 to 2 db . 



Figures 6 and 'J show how the ^wo preceding systems compare to 

 a bandlimited Eckart filter. Figure 6 indicates that tJiere is little use 

 to extend the bandwidth of an Eckart filter beyond about 2 llq , where the 

 ^1.0 are optimum bandwidths determined from Fif-nire k. Figure 7 

 indicates that a narrow bandwidth Eckart filter, with M. ^ \^^l'2-, is of little 

 value since its performance is nearly identical to the simple bandlimited 

 pre-whitening system. 



Figure 8 shows tlie losses involved in using a mismatched Eckart 

 filter, i.e., using a filter designed for cq when the signal spectrum 

 actually has a slope %.. By comparison with Figures h and ^, it can be seen 

 that the Eckart filter generally exhibits less mismatching loss than the 

 pre-whitening bandlimited system. If the designer were constrained to a 

 single shaping filter specification, i.e., he could not implement a 

 matching (Eckart) filter for each and every signal spectra, then a mis- 

 matched Eckart filter with ^0 '^•^ 2.2 would minimize the worst case loss for 

 1 - £> s 6 . The performance of such a mismatched Eckart system is compared 

 to the minimum worst -case, bandlimited, pre-whitening system in Table II. 

 When the performance of both systems is compared to a matched Eckart filter, 

 the mismatched Eckart is superior by some 1 to 2 db . 



Tlius, the following conclusions can be drawn from the numerical 

 results contained in this paper. For signal spectra which have a constant 

 slope w.r.t. noise of -10 log 2^ db/oct above some lower limit of fi cps: 



(1) Any Eckart filter implementation need not have a bandwidth 

 greater than 2 lio , where the do are determined from Figure h. 



(2) An Eckart filter, for any particular value of c^ improves 

 performance by 1 to 2 db over an optimized bandlimited pre-whitening sys- 

 tem; although not totally insignificant, the improvement is marginal. 



(3) A mismatched Eckart filter exhibits less loss than a mis- 



31 



