The near shift-invariance of the dual-tree complex wavelet transform revisited

The dual-tree complex wavelet transform (DTCWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and image processing. This paper presents a quantitative proof of the superiority of the DTCWT over the DWT in case of modulated wavelets.Comment: 15 page

Comments on "phase-shifting for nonseparable 2-D haar wavelets"

In their recent paper, Alnasser and Foroosh derive a wavelet-domain (in-band) method for phase-shifting of 2-D "nonseparable" Haar transform coefficients. Their approach is parametrical to the (a priori known) image translation. In this correspondence, we show that the utilized transform is in fact the separable Haar discrete wavelet transform (DWT). As such, wavelet-domain phase shifting can be performed using previously-proposed phase-shifting approaches that utilize the overcomplete DWT (ODWT), if the given image translation is mapped to the phase component and in-band position within the ODWT

Wavelet analysis of speech signal

This paper concerns the issue of wavelet analysis of signals by continuous and discrete wavelettransforms (CWT – Continous Wavelet Transform, DWT – Discrete Wavelet Transform). Themain goal of our work was to develop a program which, through the CWT and the DWT analyses,would obtain graph of time-scale changes and would transform it into the spectrum, that is a graphof frequency changes. In this program we also obtain spectra of Fourier Transform and LinearPrediction. Owing to this, we can compare the Wavelet Transform results to those from the FourierTransform and Linear Prediction

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's

Wavelet Estimation of Time Series Regression with Long Memory Processes

This paper studies the estimation of time series regression when both regressors and disturbances have long memory. In contrast with the frequency domain estimation as in Robinson and Hidalgo (1997), we propose to estimate the same regression model with discrete wavelet transform (DWT) of the original series. Due to the approximate de-correlation property of DWT, the transformed series can be estimated using the traditional least squares techniques. We consider both the ordinary least squares and feasible generalized least squares estimator. Finite sample Monte Carlo simulation study is performed to examine the relative efficiency of the wavelet estimation.Discrete Wavelet Transform

Perbandingan Kinerja Citra Watermarking Dengan Menggunakan Metode Discrete Wavelet Transform (DWT) Dan Discrete Cosinus Transform (DCT)

The Research we propose is to compare watermarking method using Discrete Wavelet Transform (DWT) with Discrete Cosinus Transform (DCT). From these two methods, we will see the comparison of image has been given watermarking. By looking at the results of these two methods, the owner of digital image can select the best method to protect his data based to his need. The watermarked image will be analyzed objectively by means square error (MSE) and peak-to-peak signal to noise ratio (PSNR). Then we will look at its influences after given noise degradation. The simulation results showed the Discrete Wavelet Transform (DWT) methods is the best if it is compare to Discrete Cosinus Transform (DCT)

Discrete wavelet transform-based RI adaptive algorithm for system identification

In this paper, we propose a new adaptive filtering algorithm for system identification. The algorithm is based on the recursive inverse (RI) adaptive algorithm which suffers from low convergence rates in some applications; i.e., the eigenvalue spread of the autocorrelation matrix is relatively high. The proposed algorithm applies discrete-wavelet transform (DWT) to the input signal which, in turn, helps to overcome the low convergence rate of the RI algorithm with relatively small step-size(s). Different scenarios has been investigated in different noise environments in system identification setting. Experiments demonstrate the advantages of the proposed DWT recursive inverse (DWT-RI) filter in terms of convergence rate and mean-square-error (MSE) compared to the RI, discrete cosine transform LMS (DCTLMS), discrete-wavelet transform LMS (DWT-LMS) and recursive-least-squares (RLS) algorithms under same conditions