# autocorrelation peak

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?

• 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 $s(t)$. – MBaz Jul 10 at 21:25
• 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. – Dilip Sarwate Jul 10 at 21:26

## 1 Answer

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