268 TECHNIQUES FOR SIGNAL AND NOISE ANALYSIS 



As already noted, the error is assumed zero when the spectrum of the 

 video noise is determined in order to simplify the calculations. This 

 corresponds to the case already considered in Paragraph 5-7. The spectrum 

 of the video noise is thus pictured in Fig. 5-12, and its autocorrelation 

 function is given by Equation 5-81. Dividing the noise power in the square 

 of the envelope as determined from these sources by the square of the d-c 

 level, to account for the effect of the AGC, gives the effective video noise 

 power during a pulse: 



Video noise power (with AGC) - ^[^"V^w'^!^ ' (^-92) 



With a pulse width normally on the order of a microsecond, the width of the 

 IF pass band, W cps in Fig. 5-12, must be approximately 1 Mc/sec or 

 greater. The spectrum of the video noise will also be approximately of this 

 width with a correlation time on the order of a microsecond. The repetition 

 rate on the other hand will normally lie in the range from a few hundred to 

 a thousand cps. Pulses will thus be separated by at least a millisecond, and 

 the pulse-to-pulse fluctuations due to internal noise should be very nearly 

 independent. 



The effect of the pulse stretching operation is considered next. In Para- 

 graph 5-6 the spectrum of the output of a pulse stretcher was developed 

 from an input of independent noise pulses. This is exactly the situation 

 being considered in this example. Thus the spectrum of the stretched 

 signal plus noise should have the form given by Equation 5-66 which was 

 illustrated in Fig. 5-9. If we denote the repetition period by T, the power 

 spectrum of the input to the demodulator will be of the following form: 



Noise spectrum of demodulator input 



[1 + 1{SIN)\T 

 (1 + SINY 



sinjo7y2]2 

 cor/2 J 



(5-93) 



(1 + SINY 



The effect of the demodulator on its input spectrum was established in 

 Paragraph 5-6 (Equation 5-63). The demodulator input spectrum will be 

 shifted back and forth by the demodulating frequency and multiplied by 

 the factor (1/4 k''): 



Noise spectrum at demodulator output = ' ' [A(a; + wj 



+ A^(co - CO.)]. (5-94) 



The width of each component of this spectrum is approximately 1 /T cps, 

 which normally might be on the order of a few hundred to a thousand cps. 

 Since the bandwidth of the tracking loop will normally be only a few cps, 

 only the power density in the neighborhood of zero frequency is significant; 



