NAFI TR-lUUo 

 VII. THE MSMATCHED ECKART FILTEE 



The relative performance of the pre-whitening system shown in 

 Figure k can be viewed as a plot of "mismatch" loss; i.e., if the system 

 bandwidth is matched to the signal spectrum (^i = ^,o for each 1), the loss 

 is Odb . For the simple spectral characteristics assumed in this report, 

 it is possible to make a similar plot demonstrating the effect of mismatch- 

 ing on the performance of an Eckart filter. The matching parameter for the 

 Eckart filter is, of course, not bandwidth, but the relative signal spectral 

 slope, 5. Consequently, we are interested in determining the performance 

 of an Eckart filter designed for a signal slope of ?o in an environment 

 where the actual received signal has a slope of §, not necessarily equal 

 to lo • The implications of mismatching for more realistic spectra are 

 discussed in the conclusions. 



The input signal and noise spectra are 



The shaping filter has a transfer function 



whe re 



Then the spectra into the square-law device are, by equation I3, 



uhere § = P-o-, 5o = P-Q-q. Applying equation 10 to these spectra, the 

 system output SNE is 



(?+!,-!) 



f'i, ?.'- 



