Related papers: The Basic Discrete Hilbert Transform with an Infor…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
This work addresses the problem of error concealment in video transmission systems over noisy channels employing Bregman divergences along with regularization. Error concealment intends to improve the effects of disturbances at the…
A key task in managing distributed, sensitive data is to measure the extent to which a distribution changes. Understanding this drift can effectively support a variety of federated learning and analytics tasks. However, in many practical…
The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard…
In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on…
We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is…
The change-point detection problem seeks to identify distributional changes at an unknown change-point k* in a stream of data. This problem appears in many important practical settings involving personal data, including biosurveillance,…
The analytic signal method via the Hilbert transform is a key tool in signal analysis and processing, especially in the time-frquency analysis. Imaging and other applications to multidimensional signals call for extension of the method to…
Wireless communication is susceptible to eavesdropping attacks because of its broadcast nature. This paper illustrates how interference can be used to counter eavesdropping and assist secrecy. In particular, a wire-tap channel with a…
Multirate digital signal processing and model reduction applications require computation of the frequency truncated norm of a discrete-time system. This paper explains how to compute the frequency truncated norm of a discrete-time system.…
Most differentially private (DP) algorithms assume a central model in which a reliable third party inserts noise to queries made on datasets, or a local model where the users locally perturb their data. However, the central model is…
We define a compact version of the Hilbert transform, which we then use to write explicit expressions for the partial sums and remainders of arbitrary Fourier series. The expression for the partial sums reproduces the known result in terms…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
We propose a new internal calibration process using chirp pulses. Our method is utilized to mitigate thermal drift, which is unwanted changes and usually occurs in active elements such as a high power amplifier and low noise amplifier. The…
We study the integration problem on Hilbert spaces of (multivariate) periodic functions. The standard technique to prove lower bounds for the error of quadrature rules uses bump functions and the pigeon hole principle. Recently, several new…
Heat transfer and dissipation exists in almost any physical, chemical or biological systems. Cells, as the basic unit of life, undergo continuous heat transfer and dissipation during their metabolism. The heat transfer and dissipation…
By solving Maxwell equations with the ideal-metal boundary conditions in the TM case, we have fully described the transmission and diffraction properties of a single slit regardless of its width. Efficiencies of the main transformation…
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…
In applications such as clinical safety analysis, the data of the experiments usually consists of frequency counts. In the analysis of such data, researchers often face the problem of multiple testing based on discrete test statistics,…
We study the problem of discrete distribution estimation under utility-optimized local differential privacy (ULDP), which enforces local differential privacy (LDP) on sensitive data while allowing more accurate inference on non-sensitive…