258 



TECHNIQUES FOR SIGNAL AND NOISE ANALYSIS 



^v{T) ~ 0, the autocorrelation of the output is very nearly a triangle as is 

 indicated in Fig. 5-9a. The Fourier transform of a triangular function has 



Delay Time - r 



Fig. 5-9a Autocorrelation Function of Pulse Stretcher Output with Wide-Band 



Noise Input. 



already been determined in Equation 5-21 

 spectrum of the stretched process will be 



On using that result, the power 



Nyic.) 



,^( smcoT/2 y 



V coT/2 



(5-66) 



The autocorrelation and the power spectrum of the pulse stretcher output 

 in this case are both shown in Fig. 5-9. We might note that one of the basic 

 features of this sort of operation is to concentrate the noise in a wide input 

 spectrum in a low-frequency spectrum of width approximately 1 jT cps. 



NyiOO) 



-6f -47r -27r 2ir Air Sir 



Nondimensional Angular Frequency.cof 



Fig. 5-9b Power Density Spectrum of Pulse Stretcher Output with Wide-Band 



Noise Input. 



5-7 NARROW BAND NOISE 



Signals in radar systems normally have the form of a radio-frequency 

 carrier modulated by a low-frequency envelope which contains the essential 

 intelligence. Such signals are filtered and amplified by tuned circuits with 

 bandwidths just sufficient to pass the modulation sidebands. Noise asso- 

 ciated with signals of this form or originating in circuits designed to amplify 

 such signals will have a narrow spectrum centered about the carrier. In 

 this paragraph, we shall develop some of the properties of narrow band 

 noise and signal plus noise. 



