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while I was reading J. Barry's textbook (https://www.springer.com/gp/book/9780792375487), page 308 says the following:

"... symbol-rate sampling at the matched filter output is generally at less than the Nyquist rate, so aliasing of both noise and signal is inherent in this sampling. This aliasing will not compromise the performance of the receiver as long as the filter before the sampling is a matched filter."

Here, the context of this text is about how whitened matched filter (WMF) can provide sufficient statistics for ML detector. But I do not understand why he mentions that aliasing of signal and noise does NOT degrade the system performance as long as the matched filter is deployed.

My suspicion is that noise is whitened after WMF, and hence the aliasing will simply increase the variance of the noise but does not change the autocorrelation between noise samples (here, since the noise is whitened, its autocorrelation should be 0). But the following thought was that the ISI generated by the aliasing will decrease the system performance at the end...

How am I supposed to understand this text?

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  • $\begingroup$ The key, I think, is to look at the effects of sampling and noise correlation at the exact symbol instant, which is when the output of the matched filter is observed. The output at any other time may be distorted, correlated, etc... but at the right time instant, the output is free of those effects. $\endgroup$
    – MBaz
    Apr 7 '21 at 21:07
  • $\begingroup$ Thanks MBaz. do you happen to know any articles talking about this or mathematical proof? $\endgroup$
    – Emmmm
    Apr 7 '21 at 22:20
  • $\begingroup$ Not off the top of my head at the moment, but I'm sure this is covered in Proakis. $\endgroup$
    – MBaz
    Apr 7 '21 at 22:51

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