NAFI TR-lU1^0 



Both factors on the right of equation 37 have already heen determined, 

 viz., from equations 30 and 36, so that 



$NI\^ _ i( Vj if) 



sv«/ - -7~;^v 0^) 



hi/^) 



Since we are only concerned with those cases for which optimum bandwidths 

 exist for Yj;(|a,), the value of § can be restricted to being greater than 2, 

 and no perplexing mathematical difficulties are encountered in the above 

 manipulations . 



Equation 36 is plotted in Figure 6; naturally, Tl.(p.), the loss 

 associated with bandlimiting the Eckart filter, approaches Odb as la gets 

 large, the approach being faster as 5 increases. The use of a bandlimited 

 Eckart filter with m- = l-to > the "optimum" bandwidth for each | from Figure 

 h, results in -| to 1 db of loss compared to the infinite bandwidth Eckart; 

 recall that for the conventional pre-whitening system with (i = m-o , the loss 

 was from 1 to 2 db (Figure 5)- 



Equation 38 is plotted in Figure 7- Again the results agree with 

 intuition. Where both the Eckart and pre-whitening filters have narrow 

 bandwidths, they result in approximately the same performance. For large 

 bandwidths, the factor ^[^(m.) in equation 38 approaches unity, and the 

 bandlimited Eckart out-performs the pre-whitening system by the same amount 

 as the infinite bandwidth Eckart shown in Figure 5 • 



23 



