Discrete-time signal from CT signal

Creator
Creator
Seonglae Cho
Created
Created
2023 Nov 1 2:23
Editor
Edited
Edited
2023 Nov 10 9:55
Refs
Refs
TT is important
xs[t]=xc(t)δ(tnT)=xc(nT)δ(tnT)x_s[t] = x_c(t)\sum_\infty \delta(t-nT) \newline = \sum_\infty x_c(nT)\delta(t-nT)
 
 

Relation between
CTFT
&
DTFT

xc(nT)ejωn=Xs(jω)\sum_\infty x_c(nT) e^{-j\omega n} = X_s(j\omega)
 
x[n]=xc(nT)FTXs(ejω)=x[n]ejωn=1TXc{j(ωT2πkT)}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 Xs(jω)X_s(j\omega)
 
 
 
 
 

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