Directional dual-tree complex wavelet packet transform implementation using band-limited synthetic signals

Abstract

In medicine, Doppler ultrasound is frequently used as a non invasive diagnostic technique to evaluate cardiovascular disorders. The outputs of Doppler ultrasound systems are in quadrature format and they have to be preprocessed to obtain directional blood flow signals. Later these directional signals can be analyzed to detect asymptomatic embolic signals in the cerebral circulation. Embolic signals can be considered as narrow-band (or band-limited) signals and that's why various frequency based methods such as Fourier transform and discrete wavelet transform were used to process these signals. In this study, a complex discrete wavelet packet transform, which has the ability of mapping directional information while processing quadrature signals, is introduced and its analyticity property is examined using band-limited synthetic quadrature signals.