This paper presents an algebraic approach to construct Mband orthogonal wavelet bases. A system of constraint equations is obtained for M-band orthonormal filters, and then a solution based on SVD (Singular Value Decomposition) is developed to enable us to produce innumerable wavelet bases of given length. Also the property of 2 vanishing moments is integrated into our wavelet construction proc...

We present a new class of wavelet bases—Fresnelets—which is obtained by applying the Fresnel transform operator to a wavelet basis of L2. The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and processing optically generated holograms recorded on CCD-arrays. We first investigate the multiresolution properties (translation, dilation) of the Fresnel ...

Wavelet packets have been the focus of active research for twenty years, both in theory and applications. In this work, the notion of orthogonal nonseparable five-variantl wavelet packets is introduced. A new approach for de-signing them is presented by iteration method. We proved that the fivevariant wavelet packets are of the orthogonality trait. We give three orthogonality formulas regarding...

In this paperthe eflcient implementation of different types of orthogonal wavelet transforms with respect to practical applications is discussed. Orthogonal singlewuvelet triinsfornis being based on one scaling function and one wavelet function are used for denosing of signals. Orthogonal multiwavelets are bused on several scaling filnctions and several wavelets. Since they allow properties lik...

This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step (prefiltering...

We construct oblique multi-wavelets bases which encompass the orthogonal multi-wavelets and the biorthogonal uni-wavelets of Cohen, Deaubechies and Feauveau. These oblique multi-wavelets preserve the advantages of orthogonal and biorthogonal wavelets and enhance the flexibility of wavelet theory to accommodate a wider variety of wavelet shapes and properties. Moreover, oblique multi-wavelets ca...

In this paper, we proposed a method for simultaneous noise suppression and decon-volution. The signal estimation and denoising problem was converted into a problem of model selection by using minimum description length(MDL) criterion to choose the best bases through a library of orthogonal bases. Deconvolution was then done in this best bases domain(actually the wavelet packet coeecients) to ac...

In this paper, we propose a new M-channel wavelet bases called the cosine-modulated wavelets. We first generalize the theory of two-channel biorthogonal compactly supported wavelet bases to the M-channel case. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel compactly supported wavelet bases is given. By using this condition, a family of orthog...

Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation (MCM) scheme where the sub carriers are orthogonal waves. The main advantages of OFDM are robustness against multi-path fading, frequency selective fading, narrowband interference, and efficient use of spectrum. Recently it is proved that MCM system optimization can be achieved by applying wavelet bases instead of c...

This paper proposes a new class of Hilbert pairs of almost symmetric orthogonal wavelet bases. For two wavelet bases to form a Hilbert pair, the corresponding scaling lowpass filters are required to satisfy the half-sample delay condition. In this paper, we design simultaneously two scaling lowpass filters with the arbitrarily specified flat group delay responses at ω = 0, which satisfy the hal...