Time-Frequency Analyses

We have conducted research in the area of Time-Frequency (TF) analysis. As it is shown in the following figure, TF representations can be obtained by simply selecting part of a signal using a sliding window (in red) and taking the Fourier transform. This TF tool is known as Short-Time Fourier Transform (STFT).

We can see how much more information can be obtained using the STFT and 4 components are clearly visible in the TF plane (above).

Reconstruction or synthesis can be easily done by taking the inverse Fourier transform and shifting the record to form a partial reconstruction.

Here is an example of the inverse STFT where an audio signal (from a hydrophone) is cleaned using the time varying filter shown in left bottom.

G. Thomas, and A. Brito, “Noise Suppression and Component Extraction of Underwater Acoustic Signals,” Proc. IEEE Oceans 97, October 1997, Halifax, Nova Scotia, Canada

More information about the forward and inverse TF algorithms, filtering and other quadratic TF representations such as the Wigner-Ville and Choi-Williams can be found in the following document with pages from chapter 9 of J. Sok-Son, G. Thomas, and B. C. Flores, Range-Doppler Radar Imaging and Motion Compensation, Artech House, Inc. Norwood, MA, USA, February 2001.

Implementation is very simple as can be seen in the following Matlab code for the STFT and the Inverse STFT. Feel free to use it but please quote the book chapter