The (k, a)-generalized wavelet transform is a novel addition to the class of transforms, which has gained respectable status in realm time-frequency signal analysis within short period time. Since study both theoretically interesting and practically useful, this article, we investigated several subjects for transform. First, analyze concentration on sets finite measure. In particular, prove Don...

This is a very brief introduction on the basic concepts of wavelet transform and its applications. It is certainly not possible to present comprehensive details for wavelets in a short time, only an attempt to interject some underlying features to engineers who are not yet familiarize with wavelet transform on what makes wavelet one of the most exciting useful tools as well as research areas to...

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...

We present a new approach to the construction of biorthogonal wavelet transforms using polynomial splines. The construction is performed in a “lifting” manner and we use interpolatory, as well as local quasi-interpolatory and smoothing splines as predicting aggregates in this scheme. The transforms contain some scalar control parameters which enable their flexible tuning in either time or frequ...

ing from Special Machine Features In the context of this thesis all short vector SIMD extensions feature the functionality required in intermediate level building blocks. However, the implementation of such building blocks depends on special features of the target architecture. For instance, a complex reordering operation like a permutation has to be implemented using register-register permutat...

An intelligent approach for high impedance fault (HIF) detection in power distribution feeders using advanced signal-processing techniques such as time–time and time–frequency transforms combined with neural network is presented. As the detection of HIFs is generally difficult by the conventional over-current relays, both time and frequency information are required to be extracted to detect and...

Acoustic signals pass through numerous transforms in the auditory system before perceptual attributes such as loudness and pitch are derived. However, relatively little is known as to exactly when these transformations happen, and where, cortically or sub-cortically, they occur. In an effort to examine this, we investigated the latencies and locations of cortical entrainment to two transforms p...

Abstract A time–frequency transform is a sesquilinear mapping from suitable family of test functions to on the plane. The goal quantify energy present in signal at any given time and frequency. further specified by imposing conditions such as those stemming basic transformations signals which an density should satisfy. We systematic study how properties are reflected associated evaluation origi...