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Much of signal processing involves extracting signals of interest from noise. Without noise to combat, a radar receiver could detect an echo by simple energy thresholding. In a noiseless world an infinite amount of information could be transmitted through a communications channel every second. Were it not for noise, signal classification would be reduced to dictionary lookup. Yet signals in the real world are always noisy. Radar echoes are buried under noise, making their detection impossible without sophisticated processing. . | Digital Signal Processing A Computer Science Perspective Jonathan Y. Stein Copyright 2000 John Wiley Sons Inc. Print ISBN 0-471-29546-9 Online ISBN 0-471-20059-X 5 Noise Much of signal processing involves extracting signals of interest from noise. Without noise to combat a radar receiver could detect an echo by simple energy thresholding. In a noiseless world an infinite amount of information could be transmitted through a communications channel every second. Were it not for noise signal classification would be reduced to dictionary lookup. Yet signals in the real world are always noisy. Radar echoes are buried under noise making their detection impossible without sophisticated processing. Modem signals rely on complex modulation and error correction schemes to approach the maximum rate attainable through noisy telephone lines. Due to noise signal classification is still more an art than a science. Extracting a signal from noise can rely on knowledge of the clean signal and or knowledge of the noise. Up to now we have learned to characterize clean signals in this chapter we will study the characteristics of noise. As discussed in Section 2.3 a stochastic signal cannot be precisely predicted being bound only by its statistics. What do we mean by statistics It is jokingly said that probability is the science of turning random numbers into mathematical laws while statistics is the art of turning mathematical laws into random numbers. The point of the joke is that most people take statistics to mean a technique for analyzing empirical data that enables one to prove just about anything. In this book statistics refers to something far more tangible namely the parameters of probabilistic laws that govern a signal. Familiar statistics are the average or mean value and the variance. In this chapter we will learn how noisy signals can be characterized and simulated. We will study a naive approach that considers noise to be merely a pathological example of signals not unlike
