AbstrartWavelet analysis is a new method for analyzing t h e and frequency contents of signals. We present the Fast Wavelet Transform (FWT) implemented using Rwavelets and non-circular convolutions in the analysis of Motor Unit Action Potentials (MUAPs). This method allows for the fast extraction of localized frequency components of MUAPs that may prove to be valuable in the early and accurate ...

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of...

The discrete wavelet transform (DWT) has been extensively studied and developed in various scientific and engineering fields. The multiresolution and local nature of the DWT facilitates applications requiring progressiveness and the capture of high-frequency details. However, the intensive computation of DWT caused by multilevel filtering/down-sampling will become a significant bottleneck in re...

In this article, we prove that (unit sphere, non-harmonic cone) is a Heisenberg uniqueness pair for the symplectic Fourier transform on C n . We derive spheres as well cones are determining sets spectral projections of finite measure supported unit sphere. Further, if finitely function step two nilpotent Lie group arbitrary rank, then must be zero. The latter result correlates to annihilating W...

Abstract Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on certain unit transform, which can combine any two 1D to generate new one with better performance in cryptography applications. The behavior analysis has verified this system’s effectiveness and progress. In particular, we give specific strategy...

A family of function bases is devised from a superposition of unit characteristic functions. It is shown that these simple bases can be used to perform a quantised Fourier transform. Furthermore, the transform can be implemented in an iterative scheme such that system resources are balanced in accordance with performance.

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalised by a discrete cosine transform (DCTII). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

Using the well-known fact that the Fourier transform is unitary, we obtain a class of orthogonal polynomials on the unit circle from the Fourier transform of the Laguerre polynomials (with suitable weights attached). Some related extremal problems which arise naturally in this setting are investigated.