By Boaz Porat
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A complete, useful and up to date exposition on electronic sign processing. either mathematical and beneficial, this e-book makes use of a rigorous method of aid readers research the idea and perform of DSP. It discusses sensible spectral research, together with using home windows for spectral research, sinusoidal sign research, and the impact of noise. It additionally covers FIR and IIR filters, together with particular layout methods and MATLAB instruments.
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61) - Jix(t)]2. 62) - Jix(t2)]}. Note that, whereas Jix(t) and yx(t) are functions of a single variable (the time covariance is a function of two time variables. 2 t), the Wide-Sense Stationary Signals A random signal two properties:8 1. The mean x(t) Jix(t) is called wide-sense is the same at all time points, that is, Jix (t) 2. 63) = const. 64) - t2). For a WSS signal, we denote the difference tl - t2 by T, and call it the the function Kx(T). The function Kx(T) is called the covariance function the covariance function of a WSSrandom signal is Kx(T) t2, of Thus, lag variable of x(t).
52). 48). 39). 59). We reviewed continuous-time random signals, in particular wide-sense stationary (WSS) signals. A WSS signal is characterized by a constant mean and a covariance function depending only on the lag variable. The Fourier transform of the covariance function is called the power spectral density (PSD) of the signal. The PSD of a realvalued WSS signal is real, symmetric, and nonnegative. Two examples of WSS signals are white noise and band-limited white noise. The PSD of the former is constant for all frequencies, whereas that of the latter is constant and nonzero on a finite frequency interval.
Occasionally "noise" is understood as a synonym for a random signal, but more often it is used only when the random signal is considered harmful or undesirable. 22 CHAPTER 2. REVIEW OF FREQUENCY-DOMAIN ANALYSIS in the same physical units as the random variable itself. For example, if the random variable is a voltage across the terminals of a battery, the mean and the standard deviation are measured in volts, whereas the variance is measured in volts squared. Two random variables x and y governed by a joint probability distribution have a covariance, defined by Yx,y = E[(x - Jix)(Y The covariance can be positive, negative, inequality?
A Course in Digital Signal Processing by Boaz Porat