Non-decimated Wavelet Transform for a Shift-invariant Analysis

Abstract

ABSTRACT. Due to the ability of time-frequency location, the wavelet transform has been applied in several areas of research involving signal analysis and processing, often replacing the conventional Fourier transform. The discrete wavelet transform has great application potential, being an important tool in signal compression, signal and image processing, smoothing and de-noising data. It also presents advantages over the continuous version because of its easy implementation, good computational performance and perfect reconstruction of the signal upon inversion. Nevertheless, the downsampling required in the computation of the discrete wavelet transform makes it shift variant and not appropriated to some applications, such as for signals or time series analysis. On the other hand, the Non-Decimated Discrete Wavelet Transform is shiftinvariant because it eliminates the downsampling and, consequently, is more appropriate for identifying both stationary and non-stationary behaviors in signals. However, the non-decimated wavelet transform has been underused in the literature. This paper intends to show the advantages of using the non-decimated wavelet transform in signal analysis. The main theoretical and practical aspects of the multi-scale analysis of time series from non-decimated wavelets in terms of its formulation using the same pyramidal algorithm of the decimated wavelet transform was presented. Finally, applications with a simulated and real time series compare the performance of the decimated and non-decimated wavelet transform, demonstrating the superiority of non-decimated one, mainly due to the shift-invariant analysis, patterns detection and more perfect reconstruction of a signal.

Wavelet transform-based cross-correlation in the time-delay estimation applications

“…The given approach is based on the discrete signals sequential application of two operations -the wavelet transform and the calculation of the cross-correlation function for the obtained sets of wavelet coefficients [10]. Any WT, that meets the time invariance requirements, can be used to perform the first operation [13]. Thus, non-decimated discrete wavelet transform (NDWT) [12] or continuous wavelet transform (CWT) [13] have their application.…”

“…Any WT, that meets the time invariance requirements, can be used to perform the first operation [13]. Thus, non-decimated discrete wavelet transform (NDWT) [12] or continuous wavelet transform (CWT) [13] have their application. In practice, time-series processing is carried out and computational operations are performed using microprocessor devices.…”

A Dual-Mesh Microwave Reconstruction Method Based on Compressive Sampling Matching Pursuit Algorithm

“…Based on [23], with an assumption that a multiresolution framework is specified, φ and ψ are denoted as the scaling and wavelet functions, respectively. A data vector y = (y 0 , y 1 , ..., y m−1 ) of size m forms a function f in terms of shifts of the scaling function at some multiresolution level J such that…”

“…After the discretization of the non-sparse image, a novel wavelet transformation, called the Non-Decimated Wavelet Transformation (NDWT) [23], is applied to obtain sparsity to the 2-dimensional non-sparse object. NDWT has the advantages of time-invariance and redundancy, compared to the standard orthogonal wavelet transformations.…”

A Hybrid Approach to Gender Classification using Speech Signal

“…Hence the transform has the same number of coefficients as the original signal but most of them are closer to zeroin value hence a compressed form of signal can be obtained and with a high signal quality. However, the CWT is a highly redundant transform[6].During the study Daubechies wavelet transform was used and the reason for using this transform is that it has more coefficients for every vanishing moment while as Haar wavelet transform only has two coefficients for every vanishing moment.II. BRIEF LITERATURE REVIEWAutomatic gender identification from speech is an important problem with many applications including speaker identification, speaker segmentation, and personalizing human-machine interactions.Due to the recent advancements in the techniques of voice recording, it has become possible for researchers to quantify the parameters of voice, both time related as well as frequency related.…”