Comparison of time-frequency distribution techniques using multi-component non-stationary test signals

In the course of this study, time-frequency energy distribution techniques have been compared using a series of test signals that have very specific profiles in the time frequency domain. The techniques, which are going to be examined are the Short Time Fourier Transform, Wavelet Transform, Wigner-Ville transform, Pseudo Wigner-Ville Distribution, Rihaczek and Margenau Hill distributions, Smoothed Pseudo Wigner-Ville Distribution, Choi-Williams Distribution, Born-Jordan Distribution, Zhao Atlas Marks Distribution and Baranuik Jones Optimal Radially Gaussian Kernel Method. These techniques are all a subset of the Cohen class of energy distributions. In order to examine these techniques, three test signals were used. The first signal is two chirp signals, one increasing in frequency and the other decreasing in frequency. This signal ideally should have a distinctive X shape in the time-frequency domain. The second signal is an amplitude-modulated signal with two added impulses. This ideally should have an □ shape in the time frequency domain. The final signal is the linear sum of the two signals as explained above. An ideal time frequency representation for the three signals was generated and a comparison between the techniques was taken against these ideal signals using percentile root mean squared differences. These signals are among the most difficult signals to resolve in the time-frequency domain.