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Understanding the Context
Determine the z-transform of the following signals and depict the ROC and the locations of the poles and zeros of X (z) in the z-plane: In this section special z-transform theorems that rely on contour in-tegration are presented. For most applications these theorems find little use, but there are occasions where using them can be very help-ful. These are the transform for continuous-time, infinite-duration signals (FT), and for discrete-time, finite-duration signals (DFT). The FT is most amenable to analytical insights and manipulations, and is used in analyzing analog systems.
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We’ve just seen how time-domain functions can be transformed to the Laplace domain. Next, we’ll look at how we can solve differential equations in the Laplace domain and transform back to the time domain. The Laplace transform of the step response is YY箹⣼ = 箹⣽ 0. 0. +8 (14) The Fourier Transform: Examples, Properties, Common Pairs The Fourier Transform: Examples, Properties, Common Pairs Properties: Notation Let F denote the Fourier Transform: F = F(f) Let F-1 denote the Inverse Fourier Transform: f = F-1(F)