Pseudo Affine Wigner Distributions

An example of some of my ongoing work (with Paulo Goncalves) in time-varying signal analysis is pictured below. The images are time-frequency representations of a synthetic test signal containing a variety of components (from left to right: a hyperbolic chirp, a linear chirp, a singularity, and two modulated tones). The horizontal axis of each plot corresponds to time, while the vertical axis corresponds to frequency.

At left lies the Wigner distribution. While in theory this representation boasts excellent time-frequency resolution, in practice interactions between the various signal components give rise to a complicated interference pattern. At right lies a pseudo affine Wigner distribution. The affine smoothing inherent in this representation suppresses most of the interference components and brings out the true signal structure.

• P. Goncalves, R. G. Baraniuk, Pseudo Affine Wigner Distributions: Definition and Kernel Formulation, IEEE Transactions on Signal Processing, vol. 46, no. 6, June 1998. Short version in Proceedings of IEEE ICASSP 96, Atlanta, May 1996. Abstract.
• P. Goncalves, R. G. Baraniuk, A Pseudo-Bertrand Distribution for Time-Scale Analysis, IEEE Signal Processing Letters, vol. 3, no. 3, March 1996. Abstract.

Further examples of time-frequency analysis: optimal-kernel time-frequency representations.