By Boaz Porat
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A entire, functional and up to date exposition on electronic sign processing. either mathematical and important, this e-book makes use of a rigorous method of aid readers study 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 specific layout systems and MATLAB instruments.
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Extra info for A Course in Digital Signal Processing
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.
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.
1 Summary and Complements Summary In this chapter we reviewed frequency-domain analysis and its relationships to linear system theory. 3). The Fourier transform is a mathematical operation that (1) detects sinusoidal components in a signal and enables the computation of their amplitudes and phases and (2) provides the amplitude and phase density of nonperiodic signals as a function of the frequency. 8). 10. 17). 18). We introduced a few common signals and their Fourier transforms; in particular: the delta function 6(0, the DC function 1(0, the complex exponential, sinusoidal signals, the rectangular function rect( 0, the sinc function sinc (0, and the Gaussian function.