The new class of weights called A p weights is introduced. We prove that a characterization and an unconditional basis of the weighted Lp space Lp(Rn,w(x)dx) with w ∈ A p (1 < p < ∞) are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.

In recent years wavelet based synopses were shown to be effective for approximate queries in database systems. The simplest wavelet synopses are constructed by computing the Haar transform over a vector consisting of either the raw-data or the prefix-sums of the data, and using a greedy-heuristic to select the wavelet coefficients that are kept in the synopsis. The greedy-heuristic is known to ...

The orthogonal frequency division multiplexing is used in wireless communication due to high data rate. OFDM are robustness against multi-path fading, frequency selective fading, and narrow band interference. Wavelet analysis has strong advantages over fourier transform and also allows time-frequency domain operation with flexibility. Wavelet is applied in various fields of wireless communicati...

The complicated moments of the traces of unitary and orthogonal Haar distributed random matrices are studied. The exact formulas for different values of moment and matrix orders are obtained.

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Image Fusion is a process in which combine the relevant or same information from a set of images, into a single image that is more realistic, informative and complete than the previous input images. During the past two decades, many image fusion methods have been proposed and developed. Image Fusion methods are categorized into pixel, feature, and decision levels according to the stage at which...

Since the publication, less than ten years ago, of Mallat's paper on Mul-tiresoltion Analysis Ma], and Daubechies' paper on the construction of smooth compactly supported wavelets D], wavelets had gained enormous popularity in mathematics and in the application domains. It is suucient to note that there are currently more than 10,000 subscribers to the monthly Wavelet Digest. At the same time, ...

Several studies have demonstrated the effectiveness of Haar wavelets in reducing large amounts of data down to compact wavelet synopses that can be used to obtain fast, accurate approximate query answers. While Haar wavelets were originally designed for minimizing the overall root-mean-squared (i.e., L2-norm) error in the data approximation, the recently-proposed idea of probabilistic wavelet s...

In this paper, we proposed a new method to develop secure image-encryption techniques using a logistics -based encryption algorithm. In this technique, a Haar wavelet transform was used to decompose the image and decorrelate its pixels into averaging and differencing components. The logistic based encryption algorithm produces a cipher of the test image that has good diffusion and confusion pro...

In recent years Image and Signal compression have been receiving a lot of attention by scientists and researchers in order to improve storage and transmission capabilities. In this study we have compared the performance of Kekre’s wavelet with other wavelets viz. Haar and Daubechies 2 with respect to energy in the Low-Low (LL ), Low-High (LH) ,High-Low (HL) and High-High (HH) bands. The energy ...