Analysis of the time-frequency representation using the Gamma filter
We analyze the performance of the time-frequency representation method that utilizes the Gamma filter. Gamma filter which can be implemented as a cascade of identical first order lowpass filters generates at its taps the Poisson moments of the input signal. These moments carry spectral information about the recent history of the input signal. Due to the inherent time window embedded in the Gamma filter, the moments are local both in time and frequency. Hence, they can be used to construct a time-frequency representation as an alternative to the conventional methods of short term Fourier transform (STFT), cepstrum, etc. The appeal of the proposed method comes from the fact that in the analog domain the moments are readily available as a continuous time electrical signal and can be physically measured, rather than computed offline by a digital computer. Furthermore, for a faithful representation, it is sufficient to observe the moments at the information rate (nonstationarity rate) rather than the usually higher Nyquist rate. The observed moments can be fed into an artificial neural network (ANN) for tasks like prediction, classification and identification. This work studies the performance of the proposed representation scheme as a function of the system parameters, such as; time scale, number of moments and number of bands on the estimation quality.