Question

Can you help me to solve this problem

P5.30 Let X (k) be the 8-point DFT of a 3-point sequence x(n)- 15, -4,3). Let Y(k) be the 8-point DFT of a sequence y(n). Determine y(n) when Y (k) -Ws*X(-k)s.

Answer 1

Given,

Using the circular folding and the circular shifting properties of DFT, we have

$y(n)=IDFT[W_{8}^{5k}X(-k)_{8}]$

$y(n)=IDFT[X(-k)_{8}]_{n\rightarrow (n-5)}$

$y(n)=[x(-n)_{8}\mid _{n\rightarrow (n-5)}]R_{8}(n)$

$y(n)=x(5-n)_{8}R_{8}(n)$

$y(n)=\left \{ 0,0,0,3,-4,5,0,0 \right \}$