Abstract
One area of application of the discrete wavelet transform (DWT) has been the detection and classification of physiological signals such as electroencephalography (EEG) signals. Anomalies in EEGs yield very low frequency signals which are ideal for analysis using the DWT. Anomalies in mechanical systems yield high frequency signals. The structure of the DWT makes it an un-ideal tool for the analysis of such signals. Such signals are, however, ideal for analysis using the wavelet packet transform (WPT) in which Mallat’s pyramid algorithm is applied to the multiresolution analysis (MRA) of both the approximation and detail subspaces of a signal. As a contribution to the computer-aided signal processing of non-stationary signals, this paper develops a pyramid algorithm for the discrete wavelet packet transform (DWPT) from two-scale relations for wavelet packets. The algorithm is used in the derivation of the fast Haar discrete wavelet packet transform (FHDWPT) and its inverse. It is found out that the FHDWPT is computationally as efficient as the fast Fourier transform (FFT). KEYWORDS : Wavelet, Packets, Haar, Pyramid, Algorithm.
Highlights
Wavelet-based digital signal processing techniques are superior to other techniques in the analysis of non-stationary signals (Mallat, 1989a;Burthiel, 2011; Mallat, 1989b)
The discrete wavelet transform (DWT) has been applied to the analysis of physiological signals such as electroencephalogram (EEG) signals focusing on the detection and classification of anomalies occurring in such signals [Gell-Man, 2004; Rosso, 2001]
Anomalies in EEGs produce low frequency signals which given the structure of the DWT, are ideal for analysis using the DWT
Summary
Wavelet-based digital signal processing techniques are superior to other techniques in the analysis of non-stationary signals (Mallat, 1989a;Burthiel, 2011; Mallat, 1989b). The structure of the DWT makes it un-deal for the analysis of anomalies which produce high frequency signals. Such anomalies occur in, for example, mechanical and electrical systems [Shi, 2007]. In WD only the subspace containing the low frequency information is iteratively decomposed into lower time resolution subspaces as shown in Fig.. In the WPD both the approximation (low frequency part) and the details (high frequency part) are iteratively decomposed into lower time resolution subspaces. The decomposition of the wavelet subspaces in the high frequency section of Fig. parallels that of the DWT decomposition.
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