I've been studying a kind of "introduction" for a few days now to get to talking about equalizers and ISI, and I would like to know if I have understood the things correctly or if I got confused:

For example, in PAM modulation we know that if we choose to use a rectangular pulse as the channel input (and if we do not filter well on the receive side) then that pulse on the receive side will "spread out" at the channel output interfering with adjacent pulses (the pulse tails overlap, creating so-called inter-symbol interference).

How to eliminate ISI? 3 ways:

1) Use "$\text{sinc}(x)$" pulses: by doing so, consecutive pulses will not have ISI because each will be sampled exactly at the instant when the tails of the other two (the one before and after) pass through zero.

  • This type of pulse extends to infinity (in the time domain), so we have maximum band conservation -> good
  • The ISI = 0 as just explained -> good
  • This type of pulse (extending to infinity) is not realizable physically -> bad
  • If a small timing error appears, the ISI appears -> bad

2) RRC filter: I apply a rectangular window to the $\text{sinc}(x)$ pulse and by varying the roll-off factor I adjust the trade-of between bandwidth and ISI:

  • $\alpha$ high:
    • higher truncation, pulse tails decreasing more rapidly, lower ISI -> good
    • more bandwidth will be occupied because the change is more abrupt -> bad
  • $\alpha$ small:
    • less truncation, we return to the $\text{sinc}(x)$ pulse of case 1) -> bad

3) Equalizer: a whole separate chapter I won't go into here.

If I have made mistakes please correct me, and if you want to clarify/deepen my statements please do so!

I thank you in advance.


1 Answer 1


The understanding may require some further explanation or clarification:

Sinc pulses and similar “Nyquist Pulses” do not eliminate ISI but allow us to constrain bandwidth in transmission without introducing ISI. (This is a slight distinction but as first introduced by the OP it may come across as if the purpose of such pulses is to somehow eliminate ISI that was previously there).

An RRC pulse is a “Root Raised Cosine Pulse” and on its own does introduce ISI. An RRC shaped waveform needs to be passed through a second RRC filter to then result in the “Raised Cosine” pulse shape which has no ISI. The second filter would be the matched filter in the receiver.

  • $\begingroup$ +1 -- good answer $\endgroup$
    – MBaz
    Commented Nov 8, 2023 at 1:29
  • $\begingroup$ Thank you for your response and clarification. Can you elaborate on the first part of your answer? i.e. "Sinc pulses and similar “Nyquist Pulses” do not eliminate ISI". Because I have seen several photos online that show, for example, these three sync pulses (side by side on the time axis) each sampled at the exact instant of time when the tails of the other two pulses are at 0 (or pass through zero). How do they introduce ISI? $\endgroup$
    – KaleM
    Commented Nov 8, 2023 at 20:01
  • 1
    $\begingroup$ They do not introduce ISI, but they also don't eliminate it. Eliminating it sounds like the purpose of using Nyquist pulses is to get rid of ISI that is there. Rectangular pulses (with no other pulse shaping) don't introduce ISI either. This is a subtle clarification, but I point that out as many do think the use of the pulses is just to eliminate ISI. The purpose of the pulses is to restrict bandwidth, and do that without introducing ISI. Make sense? $\endgroup$ Commented Nov 8, 2023 at 21:28
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    $\begingroup$ Also see this post: dsp.stackexchange.com/a/40098/21048 where I elaborate further on Raised Cosine Vs Root Raised Cosine and show how the RRC filter has ISI but cascading it with the second RRC filter (to get an RC response) has no ISI. $\endgroup$ Commented Nov 8, 2023 at 21:31
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    $\begingroup$ Yes that sounds correct. Except to be clear, it is not RRC pulses but RC pulses. We split the RC filter into two to get RRC pulses and that way have a matched filter in the receiver for optimum SNR. An RRC pulse alone has ISI $\endgroup$ Commented Nov 9, 2023 at 11:25

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