Related papers: Discrete Weierstrass Fourier Transform and Experim…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
The novel concept of near-field velocity sensing is proposed. In contrast to far-field velocity sensing, near-field velocity sensing enables the simultaneous estimation of both radial and transverse velocities of a moving target. A…
This paper introduces a new tool for time-series analysis: the Sliding Window Discrete Fourier Transform (SWDFT). The SWDFT is especially useful for time-series with local- in-time periodic components. We define a 5-parameter model for…
By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the time- frequency characteristics of signals which exhibit transient os-…
This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…
This work presents a new procedure to extract features of grey-level texture images based on the discrete Schroedinger transform. This is a non-linear transform where the image is mapped as the initial probability distribution of a wave…
The Dirac-{\delta} distribution may be realized through sequences of convlutions, the latter being also regarded as approximation to the identity. The present study proposes the so called pre-orthogonal adaptive Fourier decomposition…
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of…
While numerous optical methods exist to probe the dynamics of biological or complex fluid samples, in recent years digital Fourier microscopy techniques, like differential dynamic microscopy, have emerged as ways to efficiently combine…
In this paper, a new fast and low complexity transform is introduced for orthogonal frequency division multiplexing (OFDM) wireless systems. The new transform combines the effects of fast complex-Walsh-Hadamard transform (CHT) and the fast…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
Biological soft tissues encountered in clinical and pre-clinical imaging mainly consist of light element atoms, and their composition is nearly uniform with little density variation. Thus, x-ray attenuation imaging suffers from low image…
The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hierarchy with the Hellinger and the Wasserstein metrics. We…
We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.