Weighted Inverse Short-Time Fourier Transform and Denoising Filters in the Time-Frequency Plane

Abstract

The short-time Fourier transform (STFT) is a popular time-frequency analysis method and widely used in acoustics biomedical signal processing and communication. However, since the STFT is a two-dimensional distribution but the original signal is one dimension, the inverse STFT is not a one-to-one operation, which makes the filter in the STFT domain hard to design, especially for the signal whose instantaneous frequency varies fast with time. In this work, we propose a way that applies the weighted sum of the inverse Fourier transform along different vertical lines in the STFT domain to determine the inverse STFT. With the proposed method, the original signal is well reconstructed even ifwe apply the filter in the STFT domain. The proposed algorithm is robust to the variation of instantaneous frequency and the choice of the window. It will be useful for noise removal, signal decomposition, and demodulation.