Solution of Week12 Quiz Question 4
a. Linearity
Given $ v[n]=ax[n]+by[n] $
Then
$ \begin{align} V(\omega ,n) &= \sum_k v[k]w[n-k]e^{-j\omega k} \\ &= \sum_k (ax[k]+by[k])w[n-k]e^{-j\omega k} \\ &= \sum_k ax[k]w[n-k]e^{-j\omega k}+\sum_k by[k]w[n-k]e^{-j\omega k} \\ &= aX(\omega ,n)+bY(\omega ,n) \end{align} $
b. Modulation
Given $ v[n]=x[n]e^{j\omega_0n} $
