Related papers: A Kotel'nikov Representation for Wavelets
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
In the realm of signal processing, frequency and spectrum detection are fundamental tasks that can be computationally intensive. This project leverages the power of FPGAs to perform wavelet analysis on an input signal. The goal is to detect…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
In our recent work, we proposed the design of perfect reconstruction orthogonal wavelet filterbanks, called graph- QMF, for arbitrary undirected weighted graphs. In that formulation we first designed "one-dimensional" two-channel…
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
The reflectionless filter cell described in this article alleviates many system problems associated with excess out-of-band gain, impedance mismatches, and component interactions. The simplest filter cell exhibits a third-order Inverse…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data.…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…
This paper introduces a reconstruction approach for the input signal of an oversampled filter bank (OFB) when the sub-bands generated at its output are quantized and transmitted over a noisy channel. This approach exploits the redundancy…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…