NAFI TR-ll+ilO 



passive equivalent of the matched filter for active systems (l, 10, 11 ). 

 The non-optimum system performance, again as a function of bandwidth, is 

 compared to an optimal system using such an Eckart filter. 



The third optimization is a modification of the Eckart result. 

 The assumed signal and noise spectra all approach zero asymptotically as 

 the frequency approaches infinity; thus, mathematically, the Eckart 

 filter has infinite bandwidth. Physical considerations, as well as 

 curiosity, leads one to examine the effect of terminating the high 

 frequency response while retaining the Eckart filter characteristic 

 over the finite pass -band. Tlie comparison made in this third case is 

 thus between a bandlimited Eckart filter and the bandlimited non-optimal 

 conventional system, where both systems are restricted to having the 

 same bandwidth. 



The three cases illustrate the influence of various filter 

 parameters upon performance. The first case demonstrates the effect of 

 bandwidth; the second, what is to be gained from having and utilizing 

 signal information to its fullest extent; the third case combines the 

 first two, and demonstrates the influence of signal knowledge in a system 

 which similarly must be bandlimited. 



Thus, the results provide a quantitative estimate of the rela- 

 tive value of signal spectral knowledge; i.e., how much performance can 

 be improved by the insertion of an Eckart filter in place of a simple 

 bandlimiting pre-whitener . 



In order for one to have a keener appreciation for these results, the 

 next section briefly outlines the tactical passive sonar situation and 

 those factors which influence the performance of a conventional detec- 

 tion system. 



