Directional dual-tree complex wavelet packet transforms for processing quadrature signals

Abstract

Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals.

PHM Survey : Implementation of Signal Processing Methods for Monitoring Bearings and Gearboxes

“…As a generalization of the DWT, the wavelet packet transform (WPT) was introduced for their better adaptability to non-stationary signals because it can perform an adaptive decomposition of the time-frequency axis (Serbes et al, 2016) and used, for instance, for signal processing of vibration and acoustic emission signals. WPT is based on wavelet filters and the coefficients at each level can be written as:…”

Packets Wavelets and Stockwell Transform Analysis of Femoral Doppler Ultrasound Signals

“…In another way, the high frequencies are also cut into sub-bands and the decomposition tree deviate symmetrically. The wavelet packets decomposition leads to a decomposition into frequency sub-bands of the signal [9]- [11].…”

“…It was published for the first time in 1996 by Stokwell. The basic idea of this time-frequency distribution is similar to the Fourier transform sliding window, except that the amplitude and width of the analysis window are variable depending on the frequency as is the case in wavelet analysis [11]- [12]. The S-transform of a function x(t) can be defined as a transform into wavelets with a quite specific mother wavelet multiplied by a phase factor:…”

A micro emboli vs non-emboli classification system based on the directional dual tree rational dilation wavelet transform

“…MES are short-duration, unidirectional chirping sounds which occur randomly in cardiac cycle. When the frequency characteristics of the MES are considered, it is seen that they result in an increase in intensity that is focused on a small band of frequencies (behave as a narrow-band signal) in the Doppler spectrum, resulting in a bell-shaped distribution [3].…”

“…However, due to the huge computational complexity drawback of the CWT, in real-time emboli detection systems, discrete wavelet transform (DWT), which is a discretized version of the CWT, is utilized. In the DWT context, complex discrete wavelet and discrete wavelet packet transforms have been proposed in [3][4][6][7] and satisfactory results were achieved in the process of quadrature Doppler ultrasound signals. However, in all the previously proposed complex/non-complex discrete wavelet transforms, the used high-pass and low-pass filters have fixed low Q-factors resulting in poor frequency resolution.…”