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The Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.

4
votes
Instead of considering a constant signal, let us consider a rectangular window of length $2 \ell + 1$ $$w (n) = \begin{cases} 1 & \text{if } |n| \leq \ell\\ 0 & \text{otherwise} \end{cases}$$ whose …
answered Oct 28 '17 by Rodrigo de Azevedo
1
vote
Here's a much simpler method. We have $$E (z) := \frac{1}{z+4} = z^{-1} \left(\frac{1}{1 - (-4) \, z^{-1}}\right)$$ which we assume to be the $\mathcal Z$ transform of a causal discrete-time signal. …
answered Oct 14 '17 by Rodrigo de Azevedo
1
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In continuous time, we can, though it is a mathematical curiosity of little practical use. Suppose we have a smooth continuous-time signal $x$. Using the Taylor expansion, $$x (t-1) = x(t) - \dot x ( …
answered Nov 3 '17 by Rodrigo de Azevedo