Doubt: Signal detection in noise Part 1

Question

I have a confusion regarding the matched filter detection technique. I have a binary information source signal $s(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is:

$$x(t) = s(t) + w(t)$$

Then I have created a matched filter $h(t)$ as the time reversal of the source binary signal $s(t)$. How does a matched filter work?

Answer 1

You use the matched filtering technique when you search measurement data for a signal of a given form. You know the signal waveform in advance and either you are not sure if the signal is present in your data, or you see the signal and your task is to compute the signal magnitude and location. In these cases you use the matched filtering technique.

If your measurement data contains an unknown signal buried in noise, you can try and recover the waveform of this signal, with additional assumptions made about the noise nature. Often, this noise is additive white Gaussian noise, AWGN. The signal mixed with AWGN is amenable to processing with filters; filtering gives an approximate waveform of the "pure" signal. The precision of filtering -- the proximity of a recovered signal to the "pure" signal -- varies depending on the signal and noise parameters and the filter type and implementation.

Summing up: you use matched filtering when you know the signal waveform in advance or test you data to establish the presence of hypothetical signal waveforms. The waveform you test against is called template. If you want to extract the signal waveform from noisy data, you do not use matched filtering; you apply filters.