Accurate and efficient implementation of the time-frequency matched filter

The discrete time-frequency matched filter should replicate the continuous time-frequency matched filter, but the methods differ. To avoid aliasing, the discrete 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 the performance of the matched filter degrades when using the analytic, rather than real-valued, signal. This performance degradation is dependent on the signal-to-noise ratio and the signal type. In addition, the authors present a simple algorithm to efficiently compute the time-frequency matched filter. The algorithm 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 implementation of the time-frequency matched filter.