Visualizing discrete complex-valued time-frequency representations

Time-frequency analysis techniques are effective in detecting local signal structure and have been applied successfully in a wide range of fields. Different time-frequency analysis transforms yield different time-frequency spectra. However, visualizing a complex-valued time-frequency spectrum is not a trivial task as it requires graphing in a four-dimensional space: two coordinate variables time and frequency and the real and imaginary parts of the spectrum. The most common way to graph such a complex time-frequency spectrum is to plot the amplitude or magnitude spectrum and the phase spectrum separately. Such visualization may cause difficulty in understanding combined information of amplitude and phase in time-frequency domain. In this paper, we propose a new way to visualize a complex-valued time-frequency spectrum in one graph. In particular, we will describe this technique in the context of the discrete generalized Stockwell transforms for simplicity and practical usage. We show that the proposed visualization tool may facilitate better understanding of local signal behavior and become a useful tool for non-stationary signal analysis and processing applications.