Accurate and efficient implementation of the time–frequency matched filter

Abstract

The discrete time-frequency matched filter should replicate the continuoustime-frequency matched filter, but the methods differ. To avoid aliasing, thediscrete method transforms the real-valued signal to the complex-valued analytic signal. The theory for the time-frequency matched filter does not consider the discrete case using the analytic signal. The authors find that theperformance of the matched filter degrades when using the analytic, rather than real-valued, signal. This performance degradation is dependent on thesignal-to-noise ratio and the signal type. In addition, the authors present a simple algorithm to efficiently compute the time-frequency matched filter. Thealgorithm with the real-valued signal, comparative to using the analytic signal, requires one-quarter of the computational load. Hence the real-valued signal -and not the analytic signal - enables an accurate and efficient implementationof the time-frequency matched filter.