Related papers: The Basic Discrete Hilbert Transform with an Infor…
A microwave Hilbert transformer is introduced as a new component for Real-time Analog Processing (RAP). In contrast to its optical counterpart, that resort to optical fiber gratings, this Hilbert transformer is based on the combination of a…
An improved phase retrieval method based Hilbert transform is introduced to quantitatively calculate the phase distribution from distorted fringe pattern. Also phase measurement deflectomety are widely used in specular type samples. The…
We describe the structure of the resolvent of the discrete rough truncated Hilbert transform under the critical exponent. This extends the results obtained in [8].
Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase…
Differential privacy (DP) is a formal notion for quantifying the privacy loss of algorithms. Algorithms in the central model of DP achieve high accuracy but make the strongest trust assumptions whereas those in the local DP model make the…
This report presents properties of the Discrete Pulse Transform on multi-dimensional arrays introduced by the authors two or so years ago. The main result given here in Lemma 2.1 is also formulated in a paper to appear in IEEE Transactions…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
Differential Privacy (DP) has become a gold standard in privacy-preserving data analysis. While it provides one of the most rigorous notions of privacy, there are many settings where its applicability is limited. Our main contribution is in…
We study discrete distribution estimation under user-level local differential privacy (LDP). In user-level $\varepsilon$-LDP, each user has $m\ge1$ samples and the privacy of all $m$ samples must be preserved simultaneously. We resolve the…
Consider the discrete cubic Hilbert transform defined on finitely supported functions $f$ on $\mathbb{Z}$ by \begin{eqnarray*} H_3f(n) = \sum_{m \not = 0} \frac{f(n- m^3)}{m}. \end{eqnarray*} We prove that there exists $r <2$ and universal…
This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…
Dark wavefront sensing in its simplest and more crude form is a quad-cell with a round spot of dark ink acting as occulting disk at the center. This sensor exhibits fainter limiting magnitude than a conventional quad-cell, providing that…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
We prove $L^p$ estimates for the shifted bilinear Hilbert transform, with a polylogarithmic bound in the size of the shift. As applications, we obtain $r$-variation estimates for bilinear ergodic averages in the sharp range $r > 2$, a sharp…
The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by…
We propose an efficient method for demodulation of phase modulated signals via iterated Hilbert transform embeddings. We show that while a usual approach based on one application of the Hilbert transform provides only an approximation to a…
Calibration is an essential step in radio interferometric data processing that corrects the data for systematic errors and in addition, subtracts bright foreground interference to reveal weak signals hidden in the residual. These weak and…
The lack of uniqueness arising by oversampling of Fourier coefficients is shown to provide a way of transmitting hidden information. A basic encoding/decoding system, developed on the basis of such a possibility, is discussed. The system is…