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Perform the circular convolution of the following sequences x(n)={1,1,2,1}, h (n)={1,2,3,4} using DFT and IDFT methods.
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written 17 months ago by
prajapatijaimin
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Solution:
We know $X_3(k)=X_1(k) X_2(k)$
$ X_1(k)=\sum_{n=0}^{N-1} x_1(n) e^{-32 \pi k n / N} \quad k=0,1, \ldots N-1 $
Given $x_1(n)=\{1,1,2,1\}$ and $N=4$
$ \begin{aligned} & X_1(0)=\sum_{n=0}^3 x_1(n)=1+1+2+1=5 \\ & X_1(1)=\sum_{n=0}^3 x_1(n) e^{-j \pi n / 2}=1-j-2+j=-1 \\ & X_1(2)=\sum_{n=0}^3 x_1(n) e^{-j \pi n}=1-1+2-1=1 \\ & X_1(3)=\sum_{n=0}^3 x_1(n) e^{-j 3 …
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