TTT is importantxs[t]=xc(t)∑∞δ(t−nT)=∑∞xc(nT)δ(t−nT)x_s[t] = x_c(t)\sum_\infty \delta(t-nT) \newline = \sum_\infty x_c(nT)\delta(t-nT)xs[t]=xc(t)∑∞δ(t−nT)=∑∞xc(nT)δ(t−nT) Relation between CTFT & DTFT ∑∞xc(nT)e−jωn=Xs(jω)\sum_\infty x_c(nT) e^{-j\omega n} = X_s(j\omega)∑∞xc(nT)e−jωn=Xs(jω) x[n]=xc(nT)↔FTXs(ejω)=∑∞x[n]e−jωn=1T∑∞Xc{j(ωT−2πkT)}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})\}x[n]=xc(nT)FTXs(ejω)=∑∞x[n]e−jωn=T1∑∞Xc{j(Tω−T2πk)}which is simply a frequency scaled version of Xs(jω)X_s(j\omega)Xs(jω)