Practice Problem
(This problem clarifies how zero-padding a signal changes its DFT.)
let x[n] be a signal with duration N. More precisely, assume that $ x[n]=0 $ for $ n> N-1 $ and for $ n<0 $.
Let y[n] be the zero-padding of x[n] to length M>N:
$ y[n]= \left\{ \begin{array}{ll} x[n], & 0\leq n < N,\\ 0, & N \leq n <M. \end{array} \right. $
Show that the M point DFT of y[n] satisfies
$ Y_M [k] = {\mathcal X} \left( \frac{2 \pi k }{M}\right), \text{ for } k=0,1,\ldots, M-1, $
where $ {\mathcal X} (\omega) $ is the DTFT of x[n].
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
write it here.
Answer 2
write it here.
