Related papers: Time-Frequency Analysis (Lecture Notes)
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.
Most studies on speech enhancement generally don't consider the energy distribution of speech in time-frequency (T-F) representation, which is important for accurate prediction of mask or spectra. In this paper, we present a simple yet…
Quantum computing is a rapidly evolving field encompassing various disciplines such as physics, mathematics, computer engineering, and computer science. Teaching quantum computing in a concise and effective manner can be challenging,…
In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
Taking notes during lectures is one of the required skills, among many others, that students need (i) to master the topic covered in the lecture, (ii) to actively engage in the learning process with minimal to no distractions, (iii) to…
I have merged the lecture notes (in french) of two 24 hour courses I taught at the university Pierre-et-Marie Curie (Paris 6) during the first semester of the academic year 2013-2014. The first one was devoted to the general material that…
This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal…
These short lecture notes contain a not too technical introduction to point processes on the time line. The focus lies on defining these processes using the conditional intensity function. Furthermore, likelihood inference, methods of…
Motivated by analyzing complicated time series, nonlinear-type time-frequency analysis became an active research topic in the past decades. Those developed tools have been applied to various problems. In this article, we review those…
The aim of this paper is to present a set of Python-based tools to develop forecasts using time series data sets. The material is based on a four week course that the author has taught for seven years to students on operations research,…
Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the…
Time series analysis finds wide applications in fields such as weather forecasting, anomaly detection, and behavior recognition. Previous methods attempted to model temporal variations directly using 1D time series. However, this has been…
These lecture notes bridge a gap between introductory quantum field theory (QFT) courses and state-of-the-art research in scattering amplitudes. They cover the path from basic definitions of QFT to amplitudes relevant for processes in the…
The area of Fourier analysis connected to signal processing theory has undergone a rapid development in the last two decades. The aspect of this development that has received the most publicity is the theory of wavelets and their relatives,…
This in an introduction to the theory of non-commutative distributions of non-commuting operators or random matrices. Starting from the basic problem to find a good approach to the meaning of "non-commutative distribution" we will, in…
These are the notes from my courses on the arithmetic of quadratic forms.
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
Fourier methods have a long and proven track record as an excellent tool in data processing. As memory and computational constraints gain importance in embedded and mobile applications, we propose to combine Fourier methods and recurrent…