Theory and applications of adaptive constant-Q distributions

A new class of signal adaptive time-frequency representations called the adaptive constant-Q distribution (AQD) is introduced. The AQD exploits a priori knowledge about a signal's instantaneous frequency and bandwidth to perform signal-dependent smoothing of the Wigner distribution. The objective is to achieve a good tradeoff between reducing the variance and preserving the resolution by means of time-frequency dependent smoothing (specifically for use in medical Doppler ultrasound). A numerical, alias-free implementation of the AQD is presented. Deterministic, multicomponent signals as well as synthetic Doppler ultrasound signals were analyzed with the AQD. The performance of the AQD was compared with the power spectrogram, the exponential distribution, and the adaptive optimum kernel representation as well as with theory. The error was consistently lowest for the AQD. In conclusion, a new signal adaptive class of time-frequency distributions has been developed, and its potential in nonstationary signal analysis has been demonstrated.