For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including eecient numerical estimates if the number L of decomposition levels is small, as well as growth estima...

In this paper, we propose a semi-blind, imperceptible, and robust digital audio watermarking algorithm. The proposed algorithm is based on cascading two well-known transforms: the discrete wavelet transform and the singular value decomposition. The two transforms provide different, but complementary, levels of robustness against watermarking attacks. The uniqueness of the proposed algorithm is ...

Wavelet transforms have proven to be useful tools for several applications, including signal analysis, signal coding, and image compression. This paper surveys the VLSI architec-tures that have been proposed for computing the Discrete and Continuous Wavelet Transforms for 1-D and 2-D signals. The proposed architectures range from SIMD arrays to folded architectures such as systolic arrays and p...

Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonorm...

The structure and algorithm of IDFT DFT, the conventional method used in modulation/demodulation process in OFDM system, has matured today. Researchers have developed new transforms in an effort to replace this traditional structure, such as DHT-based structure (Discrete Hartley Transform) and DWT-based (Discrete Wavelet Transform) structure. In this project, all three structures will be implem...

Poor directional selectivity, a major disadvantage of the 2D separable discrete wavelet transform (DWT), has heretofore been circumvented either by using highly redundant, nonseparable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees. In this paper, we demonstrate that superior directional selectivity may be obtained with no redundancy in any separable wavele...

A major step toward the use of hyperspectral sensors to detect subpixel targets is the ability to detect constituent absorption bands within a pixel’s hyperspectral curve. This paper introduces the use of multiresolution analysis, specifically wavelet transforms, for the automated detection of low amplitude and overlapping constituent bands in hyperspectral curves. The wavelet approach is evalu...

Recently the Wavelet Transform has gained a lot of popularity in the field of signal and image processing. This is due to its capability of providing both time and frequency information simultaneously, hence giving a timefrequency representation of the signal. The traditional Fourier Transform can only provide spectral information about a signal. Moreover, the Fourier method only works for stat...

In this paper I describe an evolutionary wavelet network to optimize the filtering of a statistical time series into separate contributions. The wavelet base is regarded as a neural network where the network nodes are discrete wavelet transforms, the wavelon, and the network structure and parameters are selected through evolutionary techniques. With this combined approach I can separate stochas...

We consider equidistant discrete splines S(j), j ∈ Z, which may grow as O(|j|s) as |j| → ∞. Such splines present a relevant tool for digital signal processing. The Zak transforms of Bsplines yield the integral representation of discrete splines. We define the wavelet space as a weak orthogonal complement of the coarse-grid space in the fine-grid space. We establish the integral representation o...