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In signal processing, sampling is the reduction of a continuous-domain signal to a discrete-domain signal.

From Wikipedia: A zero-order hold reconstructs the following continuous-time waveform from a sample sequence $x[n]$, assuming one sample per time interval $T$: $$x_{\mathrm{ZOH}}(t)\,= \sum_{n … asked Feb 27 '16 by Mark 3answers The rectangular function is defined as:$$\mathrm{rect}(t) = \begin{cases} 0 & \mbox{if } |t| > \frac{1}{2} \\ \frac{1}{2} & \mbox{if } |t| = \frac{1}{2} \\ 1 & \mbox{if } |t| < \frac{1}{2}. \\ \end{c …
transform in previous equation, we obtain the Whittaker-Kotelnikov-Shannon (WKS) sampling theorem, $$f(x)=\sum_{n\in \mathbb Z}f(n) \operatorname{sinc}(x-n), \ \ \ x\in \mathbb R$$ where $\operatorname{sinc … }(x)$ is the normalized sinc function. My question is the following. Sampling theorem, at least in the version that I wrote above, is related to $L^2$ space and so, to scalar product: $$\langle g, h … asked Sep 24 '15 by Mark 1answer From Wikipedia: A zero-order hold reconstructs the following continuous-time waveform from a sample sequence x[n], assuming one sample per time interval T:$$x_{\mathrm{ZOH}}(t)\,= \sum_{n …