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GATE IN 2024 | Question-43

The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular convolution of $x[n]$ and $y[n]$, the value of $z[0]$ is (rounded off to nearest integer).

Note: The DFT of a $N$-point sequence $x[n]$ is defined as
\[
X[k]=\sum_{n=0}^{N-1} x[n] e^{\frac{-j 2 \pi n k}{N}}
\]

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