By Boaz Porat
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A complete, sensible and up to date exposition on electronic sign processing. either mathematical and invaluable, this booklet makes use of a rigorous method of support readers examine the idea and perform of DSP. It discusses functional spectral research, together with using home windows for spectral research, sinusoidal sign research, and the influence of noise. It additionally covers FIR and IIR filters, together with precise layout techniques and MATLAB instruments.
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This framework, called the theory of distributions, is beyond the scope of this book; see Kwakernaak and Sivan [1991, Supplement C] for a relatively elementary treatment of this subject. We shall continue to use the delta function but not in rigor, as common in engineering books. 4. [po 13] A common misconception is that every LTI system has an impulse response. The following example shows that this is not true. Let x(t) be in the input family if and only if (1) x(t) is continuous, except at a countable number of points t; (2) the discontinuity at each such point is a finite jump, that is, the limits at both sides of the discontinuity exist; (3) the sum of absolute values of all discontinuity jumps is finite.
We shall limit ourselves to real-valued random signals. A continuous-time random signal (or random process) is a signal x(t) whose value at each time point is a random variable. Random signals appear often in real life. Examples include: 1. The noise heard from a radio receiver that is not tuned to an operating channel. 2. The noise heard from a helicopter rotor. 3. Electrical signals recorded from a human brain through electrodes put in contact with the skull (these are called electroencephalograms, or EEGs).
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).
A Course in Digital Signal Processing by Boaz Porat