Detecting non-stationary signals using fractional Fourier methods

Signal processing methods have been developed over the last 60 years to detect and analyse complicated non-stationary signals, such as speech and seismic activity. The traditional method for analysing such signals is through a spectrogram based on the short-time Fourier transform (STFT). However, the STFT is not ideal since it reflects only the stationary properties contained in any short time-segment of the signal. Other methods, such as wavelet transforms and Wigner-Ville distributions, which have found favour in speech processing, inevitably produce cross-term interference resulting in the appearance of false signals. New processing techniques are required to produce improved spectrograms for analysis of nonstationary signals. Recently, spectrograms based on the fractional Fourier transform (FrFT) were shown to give better time-frequency resolution of signals containing a non-stationary components, such as a linear chirp. However, current FrFT methods are not always ideally suited to signals containing multiple non-stationary components. In this paper, we present an improved spectrogram based on the FrFt, which accounts for signals with multiple non-sationary components. To demonstrate the superior time-frequency resolution of such signals using our improved spectrogram, we analyse signals containing multiple non-stationary components, including an artifical signal and a bat echolocation signal.