Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
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TL;DR: In this article, it was shown that the truncation error can also be removed at discrete frequencies, simply by first subtracting a ramp from the step response of a network, with consequent noise enhancement.
Abstract: If the discrete Fourier transform of the step response of a network is taken, a large truncation error results, since only a finite number of samples is used. This error is usually removed by first differentiating the waveform, with consequent noise enhancement. The letter shows that the error may also be removed at discrete frequencies, simply by first subtracting a ramp from the step response.
91 citations
90 citations
Book•
18 May 2001TL;DR: The Fourier Transform Transform Integrals on Infinite Intervals (FITI) as discussed by the authors is a classical Fourier transform that is used in the analysis of the Fourier series.
Abstract: PRELIMINARIES The Starting Point Basic Terminology, Notation, and Conventions Basic Analysis I: Continuity and Smoothness Basic Analysis II: Integration and Infinite Series Symmetry and Periodicity Elementary Complex Analysis Functions of Several Variables FOURIER SERIES Heuristic Derivation of the Fourier Series Formulas The Trigonometric Fourier Series Fourier Series over Finite Intervals (Sine and Cosine Series) Inner Products, Norms, and Orthogonality The Complex Exponential Fourier Series Convergence and Fourier's Conjecture Convergence and Fourier's Conjecture: The Proofs Derivatives and Integrals of Fourier Series Applications CLASSICAL FOURIER TRANSFORMS Heuristic Derivation of the Classical Fourier Transform Integrals on Infinite Intervals The Fourier Integral Transforms Classical Fourier Transforms and Classically Transformable Functions Some Elementary Identities: Translation, Scaling, and Conjugation Differentiation and Fourier Transforms Gaussians and Other Very Rapidly Decreasing Functions Convolution and Transforms of Products Correlation, Square-Integrable Functions, and the Fundamental Identity of Fourier Analysis Identity Sequences Generalizing the Classical Theory: A Naive Approach Fourier Analysis in the Analysis of Systems Gaussians as Test Functions, and Proofs of Some Important Theorems GENERALIZED FUNCTIONS AND FOURIER TRANSFORMS A Starting Point for the Generalized Theory Gaussian Test Functions Generalized Functions Sequences and Series of Generalized Functions Basic Transforms of Generalized Fourier Analysis Generalized Products, Convolutions, and Definite Integrals Periodic Functions and Regular Arrays General Solutions to Simple Equations and the Pole Functions THE DISCRETE THEORY Periodic, Regular Arrays Sampling and the Discrete Fourier Transform APPENDICES
90 citations
TL;DR: A new signal-adaptive joint time-frequency distribution for the analysis of nonstationary signals is proposed, based on a fractional-Fourier-domain realization of the weighted Wigner distribution producing auto-terms close to the ones in the WignER distribution itself, but with reduced cross-terms.
90 citations
TL;DR: The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform, providing new insight into wave propagation and spherical mirror resonators.
Abstract: The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems.
90 citations