Choi-Williams transform and atomic functions in digital signal processing

The appropriateness of applying the Choi-Williams transform in signal analysis was studied and compared to the Wigner transform, to the conventional windowed Fourier transform (WFT), and to AF. The Choi-Williams transform of a signal has the form where the asterisk denotes the operation of complex conjugation. The Choi-Williams transform in signal analysis has various advantages such as it provides complete information about the signal, it enables one to analyze the time-frequency content of individual singularities of the signal, and makes it possible to analyze the corresponding FSD of the signal. Choi-Williams transform, which has a high time-frequency resolution, is most commonly performed by means of numerical calculations using computer algebra systems. It can also be used in the analysis of new classes of signals, based on AF, Kravchenko-Rvachev windows, R-functions, and wavelets, because such signals are localized in the time domain.