NAFI TR-li+i|0 



matched pre-whitenint:'; system. If a minimum worst case loss criterion is 

 used to specify jj,, the bandwidth of the pre -whitening system, and §o , the 

 "matching parameter" of the Eckart filter, the Eckart design is superior 

 by 1 to 2 db. Again, the improvement appears marginal. 



The precedin,'- results and conclusions are strictly valid only 

 for the assumed simple spectral characteristics; liowever, the overall trends 

 exhibited lead one to formulate hypothesized generalizations. The impli- 

 cations for conventional system design can be stated succinctly in one 

 sentence: an intelligent choice of operating band is sufficient. The 

 remainder of this section presents an expanded discussion of this thought. 



This report basically constitutes a study of the significance 

 of signal spectral characteristics upon the performance of a conventional 

 passive detection system. Generally, the vicissitudes of the sonar environ- 

 ment are such that a detailed knowledge of signal characteristics is not 

 possible. Under these conditions, an Eckart filter implementation is not 

 practically feasible. Tlie results in this report suggest two possible sub- 

 optimum systems: the first is a conventional pre-whitening system with 

 a bandv7idth chosen to minimize the worst case loss ovei- i:ne expected rangt; 

 of signal variations; the second is a mismatched (band -limited) Eckart 

 filter with a transfer function again chosen to minimize worst case loss. 

 Of these two, the first is probably more practical. This is because real- 

 istic estimates of signal spectra are not susceptible to a simple character- 

 ization, as by a single parameter 5- Propagation effects can markedly 

 alter the behavior of Si (f) , and it would be difficult to make a plot such 

 as Figure 8; because of the complicated behavior of 3i (f) , the phrase 

 "mismatched Eckart filter" is almost meaningless. It is likely that there 

 would, exist a compromise filter that provides better worst case performance 

 than the pre-whitening system, but the likelihood of such a filter being 

 found by trial and error methods is probably small. ■'^ Further, the results 

 in this report imply that the available improvement in performance is rather 

 small. Consequently, there appears to be considerable justification for 

 being content with the design of a conventional system under the constraint 

 that the shaping filter perform only the function of pre-whitening the 



*See Appendix D(2) , 



33 



