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Can someone explain in simple words /graphs the necessary and sufficient Nyquist criterion for zero ISI in frequency domain, namely:

The constant folded Fourier Transform.

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    $\begingroup$ Do you have a reference for where you are seeing this term: "The constant folded Fourier Transform"? $\endgroup$ – Robert L. Nov 29 '18 at 21:46
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    $\begingroup$ I'd suggest trying to explain in more detail what it is that you don't understand. Any general explanations and figures we can present will be very similar to those already present on countless websites and textbooks. $\endgroup$ – MBaz Nov 29 '18 at 21:57
  • $\begingroup$ "Digital Communication Receivers, Synchronization, Channel Estimation, and Signal Processing" by Heinrich Meyr, page 65-66 $\endgroup$ – Hatem Tawfik Nov 29 '18 at 21:57
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    $\begingroup$ What @MBaz said: not many of us will have that book, and you'll need to explain what you don't understand, because otherwise our explanation would be similar to the book, and hence, likely a waste of time. $\endgroup$ – Marcus Müller Nov 29 '18 at 22:42
  • $\begingroup$ How does a flat folded spectrum look like vs an example of a non-flat folded spectrum? Is there a plot that compares both? $\endgroup$ – Hatem Tawfik Nov 29 '18 at 23:53
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The short answer is you will see that when you follow that symmetry, the resulting transform (the impulse response in time) will all have nulls spaced at T where T is the symbol duration which by definition is zero-ISI. Work through those transforms as well as ones without such symmetry and I believe it will become very clear to you what is going on. The simplest case to start is obvious: a rectangular function in one domain is a Sinc function in the other. If it is a rectangular function with width 1/T in frequency, it is a SInc in time with nulls at integer multiples of T.

Another very simple example is to then convolve the two rectangular fucntions in frequency to get a triangular fucntion which will have this "folded frequency" relationship. This is simply multiplying in time, so although we changed the Sinc response, we have not changed the location of the nulls.

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