Related papers: Time-Frequency Analysis (Lecture Notes)
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
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…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
This article describes a laboratory or demonstration technique employing the bass guitar and a Vernier LabPro (or a PC soundcard) for teaching wave physics and introducing Fourier analysis. The Fourier transform of an open string provides a…
Over 1100 students over four semesters were given the option of taking an introductory undergraduate statistics class either by in-person attendance in lectures or by taking exactly the same class (same instructor, recorded lectures,…
Special Relativity is taught to physics sophomores at Johns Hopkins University in a series of eight lectures. Lecture 1 covers the principle of relativity and the derivation of the Lorentz transform. Lecture 2 covers length contraction and…
There is a critical need to develop new educational technology applications that analyze the data collected by universities to ensure that students graduate in a timely fashion (4 to 6 years); and they are well prepared for jobs in their…
Some 50~years ago, physicists, and after them the entire world, started to found their time reference on atomic properties instead of motions of the Earth that have been in use since the origin. Far from being an arrival point, this…
We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and…
We propose two experiments suited for high school and/or undergraduate physics laboratory which are aimed to the discovery of the practical meaning and usefulness of the FFT analysis as a mathematical and graphical instrument, intended to…
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…
During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields, spanning a wide range from acoustics to optics. While…
The study of classical waves in time-periodic systems is experiencing a resurgence of interest, motivated by their rich physics and the new engineering opportunities they enable, with several analogies to parallel efforts in other branches…
These are extended lecture notes for a mini course at the Spring School on Non-Archimedean Geometry and Eigenvarieties held at Heidelberg University in March 2023. The goal of the course is to explain a modern take on the eigenvariety…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…