260 TECHNIQUES FOR SIGNAL AND NOISE ANALYSIS 



periodic pulsing of the carrier. In such systems, the signal, when it is 

 present, is a constant amplitude sinusoid. Noise will normally be present 

 with a spectrum centered about the carrier frequency and a width deter- 

 mined by the amplifiers which are designed to transmit the modulation 

 sidebands. The ratio of the bandwidth to the carrier frequency is normally 

 very small. Thus the noise can be considered narrow band noise with the 

 representation and characteristics described above. 



When a signal is present, it is assumed to be of the form 



Signal = a cos wj. (5-70) 



The peak signal power is denoted by 6" = a} jl.. The noise power is denoted 

 by A^ = 0"^ so that the signal-to-noise power ratio when the signal is present 

 is 



SIN = ay2a\ (5-71) 



With the narrow band noise represented as in Equation 5-67, the signal plus 

 noise has the form 



Signal plus noise = {a -{- x) cos wj + jy sin o^J. (5-72) 



A typical power spectrum of a c-w signal plus noise is shown in Fig. 5-10. 



I 5 6 -Function Continuous 



t Signal ^^ Noise 



i I Spectrum i^^Spectrum 



— COc ^c 



Angular Frequency 

 Fig. 5-10 Power Density Spectrum of CW Signal Plus Narrow-Band Noise. 



General operations upon radar signals to extract desired information or 

 to transform the signals into a more useable form are often referred to as 

 demodulation or detection operations as discussed in Chapter 1. The simplest 

 and most common such operation consists in the generation of the envelope 

 of a narrow band signal by means of a rectifier. In superheterodyne receivers, 

 this operation corresponds to the action of the second detector. The 

 envelope output of the second detector is most often referred to as the video 

 signal since it is commonly used as an input of some sort of visual display. 

 In the following brief analysis, we shall develop some of the more important 

 features of video signals and noise. 



The envelope of narrow band signal plus noise can be exhibited by 

 rewriting the expression in Equation 5-72 in the following form: 



