IV. CASE 1: BAEDWIDTH OPTIMIZATION IN tffllTE NOISE 



In order to obtain numerical results, some functional form 

 must be assumed for the input signal and noise spectra, Si(f) and Ni (f ) 

 in Figure 2, Since many of the quantities in the sonar equation can be 

 conveniently represented by a db/octave slope over the region of interest, 

 the following dependence is assumed: 



The spectra are thus assumed to be sharply bandlimited, and to be charac- 

 terized by constant db/octave slopes within the band (fi, fi + w) , This 

 is an oversimplified representation, particularly for Si (f ) because of 

 the propagation effects mentioned earlier; however, when tempered by 

 reason, the results from such spectra shed light upon passive system 

 performance , 



The spectra into the square -law device are 



To whiten. the noise, the shaping filter must be of the form^ 



where |=0-a is the input signal spectral slope with respect to the in- 

 put noise spectral slope, i.e., the slope of the signal spectrum into 

 the square-law device. 



The direct application of equation (lO) to the spectra in 

 equation (15) results in /- 1 6 ? . y 



*The arbitrary multiplicative constant is chosen to be unity for 

 simplicity. 



13 



