Discrete Time Response

The questions below are due on Thursday April 03, 2025; 02:00:00 PM.
 
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Find the discrete-time signal whose DTFT is

H(\Omega)=\begin{cases} 1 & \text{if}~|\Omega|\lt{\pi\over2}\\ 0 & \text{if}~{\pi\over2}\lt|\Omega|\lt{3\pi\over2} \end{cases}

and H(\Omega) is periodic in \Omega with period 2\pi.

Enter an expression for h[0]:
h[0] =~

Enter an expression for h[n], n\neq 0:
h[n]\big|_{n\ne0} =~

Assume that H(\Omega) defined above represents the frequency response of a discrete-time system. Determine the response y[n] when the input x[n] is given by

x[n] = \begin{cases} 1 & \text{if}~n=0\\ 0 & \text{if}~n=1~\text{or}~n=2 \end{cases}

and x[n] is periodic in n with period 3.

Enter the values of y[n] for -1\le y\le 4 as a list:
[y[-1],y[0],y[1],y[2],y[3],y[4]] =~