The wavelet transform is a widely used time-frequency tool for signal processing. However, with some rare exceptions, its use in signal processing is limited to discrete-time critically sampled transforms, which are particular cases of subband coding. On the other hand, interest in continuous wavelet analyses has been repeatedly demonstrated in the literature. However, implementation challenges...

We describe segmented multiresolution analyses of [0; 1]. Such multiresolution analyses lead to segmented wavelet bases which are adapted to discontinuities, cusps, etc., at a given location 2 [0; 1]. Our approach emphasizes the idea of average-interpolation { synthesizing a smooth function on the line having prescribed boxcar averages. This particular approach leads to methods with subpixel re...

-Motor Current Signature Analysis (MCSA) has been successfully used for fault diagnosis in induction machines. The current spectrum of the induction machine for locating characteristic fault frequencies is used in MCSA. The spectrum is obtained using a Fast Fourier Transformation (FFT) that is performed on the signal under analysis. The fault frequencies occur in the motor current spectra are u...

We propose the design of a hearing aid device based on the wavelet transform. The fast wavelet transform is used to decompose speech into diierent frequency components. This paper presents the diiculties in the use of wavelet transforms for speech processing, and shows how the careful selection of wavelet coeecients can enable the four major categories of speech-voiced speech, plosives, fricati...

Invertible wavelet transforms that map integers to integers are important for lossless representations. In this paper, we present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless im...

We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.

Wavelet transforms have been widely applied to image and video compression but they also have the ability to compress operators. A result is that there is great potential for producing fast algorithms for the processing of wavelet compressed image and video data. We examine the implementation of a set of fundamental image operations including pixel-wise arithmetic operators and arbitrary linear...

Near-best and best wavelet packet transforms were compared with wavelet transforms for the compression of polysomnograms in a low bitrate telemonitoring application. Near-best wavelet packet transforms provided better overall performance with respect to efficiency of computation and compression, and amenability for use in more sophisticated quality-on-demand algorithms. Keywords— near-best base...

Wavelet transforms, when combined with quantization and a suitable encoding, can be used to compress images eeectively. In order to use them for image library systems, a compact storage scheme for quantized coeecient wavelet data must be developed with a support for fast subregion retrieval. We have designed such a scheme and in this paper we provide experimental studies to demonstrate that it ...