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For any (local) observable $\mathcal{O}$, its expectation value is defined as $$ \langle \mathcal{O} \rangle = \frac{1}{Z}\int \mathcal{D}\Phi\mathcal{O}\mathrm{e}^{-S_E[\Phi]}$$ where $$ Z = \int \mathcal{D}\Phi\mathrm{e}^{-S_E[\Phi]}$$ is indeed called the partition function. My writing $S_E$ is intended to show that this is for a Euclidean theory ...


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I believe OP is asking about the matched filter of signal processing, and another implementation called a correlation receiver. I believe this is off-topic on this site, but I'll keep you from having to go elsewhere to get your question answered. Briefly, the correlation receiver does the following: Multiplies the input signal by a basis waveform ...



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