In this appendix, we derive the expression for the matched filter that optimizes the signal-to-noise ratio for a given signal. We show that the matched filter is directly proportional to the signal shifted in time divided by the noise power and thus is matched to the signal and the noise.

Inspec keywords: matched filters; signal processing; Hilbert transforms

Other keywords: signal-to-noise ratio; optimisation; noise power; matched filter; signal shifting

Subjects: Integral transforms; Signal processing and detection; Filters and other networks