GATE ECE 2024 | Question: 49

Question

The relationship between any N-length sequence $x[n]$ and its corresponding $\mathrm{N}$-point discrete Fourier transform $X[k]$ is defined as
\[
X[k]=\mathcal{F}\{x[n]\} .
\]

Another sequence $y[n]$ is formed as below
\[
y[n]=\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}\} .
\]

For the sequence $x[n]=\{1,2,1,3\}$, the value of $Y[0]$ is $\_\_\_\_\_\_\_\_\_$.