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enter image description hereenter image description here I started it but didn't how to continue , any help ?

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The best answer I could give is just a hint: think about what is the inverse discrete time Fourier transform of $X(e^{j\omega})$. Constants in the frequency domain are what in the time domain? Answering that will lead you to the answer of this question.

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  • $\begingroup$ I got x[n] = sinc(pi*n) , then exp(-(nT)^2) = 1 and that is not possible for any value of T unless n = 0. Is that correct ? $\endgroup$ – John_HB Oct 25 '19 at 20:33
  • $\begingroup$ No. A constant in frequency is not a sinc in time domain. $\endgroup$ – Engineer Oct 26 '19 at 1:33
  • $\begingroup$ It is a dirac, but how can i compare it to the first signal ? $\endgroup$ – John_HB Oct 26 '19 at 20:20
  • $\begingroup$ I think it is true for T = pi and n=0 !! $\endgroup$ – John_HB Oct 26 '19 at 20:27
  • $\begingroup$ Yes, it is an impulse. So, how can you sample $x(t)$ so that $x(nT)=1$ for $n=0$ and $x(nT)=0$ for all other values of n? HINT: try plotting it $\endgroup$ – Engineer Oct 27 '19 at 21:25

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