As the number of applications and use of wavelet transforms continues to grow, so does the number of classes and variations of wavelet transform algorithms. All of these algorithms incorporate a filter convolution in some implementation, typically, as part of an iterated filter bank. In contrast to implementations of the classical Fourier transform where there is at most a choice of sign and no...

Image data require huge amounts of disk space and large bandwidths for transmission. Hence, imagecompression is necessary to reduce the amount of data required to represent a digital image. Thereforean efficient technique for image compression is highly pushed to demand. Although, lots of compressiontechniques are available, but the technique which is faster, memory efficient and simple, surely...

In this work, we are interested in developing a speech denoising tool by using a discrete wavelet packet transform (DWPT). This speech denoising tool will be employed for applications of recognition, coding and synthesis. For noise reduction, instead of applying the classical thresholding technique, some wavelet packet nodes are set to zero and the others are thresholded. To estimate the non st...

In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and ...

As one of the major directions in applied and computational harmonic analysis, the classical theory of wavelets and framelets has been extensively investigated in the function setting, in particular, in the function space L2(R). A discrete wavelet transform is often regarded as a byproduct in wavelet analysis by decomposing and reconstructing functions in L2(R) via nested subspaces of L2(R) in ...

We suggest a new approach to wavelet threshold estimation of spectral densities of stationary time series. It is well known that choosing appropriate thresholds to smooth the periodogram is difficult because non-parametric spectral estimation suffers from problems similar to curve estimation with a highly heteroscedastic and non-Gaussian error structure. Possible solutions that have been propos...

Classical reliability assessment methods have predominantly focused on probability and statistical theories, which are insufficient in assessing the operational reliability of individual mechanical equipment with time-varying characteristics. A new approach to assess machinery operational reliability with normalized lifting wavelet entropy from condition monitoring information is proposed, whic...

Classical spectral analysis in statistics considers decomposition of stationary time series into sinusoidal components. The autocovariance and the spectrum are fundamental elements for analyzing a given time series both in time and frequency domain. However, in practice one frequently observes nonstationary time series. In order to apply spectral analysis to these processes, an extension of the...