R. S. RAV 



CHAPTER 5 



TECHNIQUES FOR SIGNAL AND NOISE 

 ANALYSIS 



5-1 INTRODUCTION 



The performance of radar systems can often be determined only by 

 tracing the received signal and corrupting noise in detail through the 

 individual system components in order to establish the cumulative effect 

 of each operation. In this chapter, some of the mathematical methods of 

 signal and noise analysis which are appropriate for studies of this kind will 

 be developed and their application illustrated with several examples. These 

 examples will include a discussion of the characteristics of signal plus noise 

 after undergoing some common nonlinear operations, the erratic perform- 

 ance of an angle tracking system in response to internally generated noise, 

 the clutter cancellation which can be achieved with a moving target 

 indicator (MTI system) and the characteristics of a matched filter radar. 



Noise analysis embodies a generalization of classical Fourier methods 

 which recognizes the statistical properties of random noise. Much of this 

 material will be presented briefly. More detailed discussions can be found 

 in the referenced literature. ^~^ 



5-2 FOURIER ANALYSIS 



To develop the theory and methods of noise analysis several basic ideas 

 relating to the representation of functions in terms of their frequency 

 components as Fourier integrals are required. This paragraph explains 

 and illustrates the concepts of: 



1. Fourier integrals or transforms and inverse transforms. 



2. Energy density spectra. 



3. Transfer functions and impulse responses. 



'S. O. Rice, "Mathematical Analysis of Random Noise," Bell System Tech. J. 23. 



2J. L. Lawson and G. E. Uhlenbeck, "Threshold Signals," Chap. 2 (Radiation Laboratory- 

 Series) McGraw-Hill Book Co., Inc., New York, 1950. 



"P. M. Woodward, Prohabilily and Information Theory .vith Applications to Radar, McGraw- 

 Hill Book Co., Inc., New York, 1953. 



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