An improved spectrogram using the multiangle centered discrete fractional Fourier transform

The spectrogram is a useful tool for the time-frequency analysis of non stationary signals. This tool, however, is based upon a multicomponent sinusoidal model over a signal analysis frame and is not suitable when, for example, the frequency content over the frame is chirping. Recently, the centered version of the discrete fractional Fourier transform was shown to possess the capability to concentrate a linear chirp signal in a few transform coefficients. We present a modified version of the spectrogram which incorporates the centered discrete fractional Fourier transform and its multiangle version and which instead decomposes the signal over the analysis frame into multiple chirp signals. We present simulation results that study the efficiency of this improved spectrogram and its application to the analysis of harmonically related chirps and bat echolocation signals.