Design of a time-frequency domain matched filter for detection of non-stationary signals

In this paper, a practical and effective approach is proposed to detect a transient or nonstationary signal component of interest from a composite signal waveform. The detection problem has been re-formulated in terms of time-frequency analysis, and, thus, the conventional 1-D (i.e., time-domain) matched filter approach is extended to the 2-D (here, time-frequency domain) optimal filtering. For that purpose, the reduced interference distribution (RID) algorithm, the outer product expansion of the time-frequency distribution, the singular value decomposition (SVD), and a priori available time-frequency information of a signal part of interest are employed to derive a time-frequency domain matched filter by utilizing the singular values of the sampled time-frequency distribution and the corresponding fractions of signal energy. Finally, one real problem of detecting the snare drum sound event from a measured musical signal is considered to demonstrate the performance of the proposed approach.