Discrete-time signal from CT signal

Creator

Created

2023 Nov 1 2:23

Editor

Edited

2023 Nov 10 9:55

Refs

T

is important

x_s[t] = x_c(t)\sum_\infty \delta(t-nT) \newline = \sum_\infty x_c(nT)\delta(t-nT)

\sum_\infty x_c(nT) e^{-j\omega n} = X_s(j\omega)

x[n] = x_c(nT) \newline \xleftrightarrow{FT} \newline X_s(e^{j\omega}) = \sum_\infty x[n]e^{-j\omega n} = \frac{1}{T}\sum_\infty X_c\{j(\frac{\omega}{T} - \frac{2\pi k}{T})\}

which is simply a frequency scaled version of

X_s(j\omega)

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