SIGNAL REPRESENTATION USING ADAPTIVE NORMALIZED GAUSSIAN FUNCTIONS

In this paper, a new joint time-frequency signal representation, the adaptive Gaussian basis representation (AGR), is presented. Unlike the Gabor expansion and the wavelet decomposition, the bandwidth and time-frequency centers of the localized Gaussian elementary functions h(p)(t) used in the AGR can be adjusted to best match the analyzed signal. Each expansion coefficient B(p) is defined as the inner product s(p)(t) and h(p)(t), where s(p)(t) is the remainder of the orthogonal projection of s(p-1)(t) onto h(p-1)(t). Consequently, the AGR not only accurately captures signal local behavior, but also has a monotonically decreasing reconstruction error parallel-to s(p)(t) parallel-to 2. By combining the AGR and the Wigner-Ville distribution, we further develop an adaptive spectrogram that is non-negative, cross-term free, and of high resolution. Finally, an efficient numerical algorithm to compute the optimal Gaussian elementary functions h(p)(t) is discussed.