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P = n, an is divergent. 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.
Understanding the Context
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. 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.
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Key Insights
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)