First-Order Recursive Smoothing of Short-Time Power Spectra in the Presence of Interference

In this letter we derive an optimal time-varying smoothing factor for smoothing non-stationary power spectra of a target signal when a noisy observation of this signal is given. The proposed approach is based on a complex Gaussian signal model in the short-time discrete Fourier domain and on mean squared error optimization. We find that the optimal smoothing factor depends on the signal-to-noise ratio as well as on the deviation between the smoothed estimate and the target signal power spectra. We investigate the properties of the proposed adaptive smoothing system and demonstrate its utility in a basic validation experiment.