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Let $s(t)$ a signal of duration $T_s$ on a bandwidth $B$. The matched filtering of this signal gives: $R=max|s(t) \ast s^{\ast}(-t)|$ and here theoretically I saw that $R=BT_s$.

But does anyone know of rigorous proof of this result?

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  • $\begingroup$ There are two incorrect claims here. One is that that the matched filter output is a scalar (it is actually another signal). The second is that the value you give for $R$ is wrong; for example, the matched filter's output depends on the energy of $s(t)$. $\endgroup$ – MBaz Jul 10 at 21:25
  • $\begingroup$ I think you are mixing up two different concepts that unfortunately use the same letter of the alphabet. The latter $R$ seems to be a rate; the former an autocorrelation value. $\endgroup$ – Dilip Sarwate Jul 10 at 21:26
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The autocorrelation itslef is a continuous signal which is sampled at the symbol rate to get the peak /Max.

Then you are talking about the symbol/bit rate which ofcourse in a noiseless scenario will be close to the channel capacity

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