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Harmonic analysis

About: Harmonic analysis is a research topic. Over the lifetime, 8530 publications have been published within this topic receiving 149765 citations.


Papers
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Journal ArticleDOI
01 Jan 1978
TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

7,130 citations

Book
01 Jan 1963
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and prices and other details are subject to change without notice. All errors and omissions excepted.
Abstract: The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. E. Hewitt, K.A. Ross Abstract Harmonic Analysis

4,348 citations

Book
15 Dec 2000
TL;DR: The topics range from the elemen- tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita- tive methods in time-frequency analysis and the theory of pseudodifferential operators.
Abstract: Time-frequency analysis is a modern branch of harmonic analysis. It com- prises all those parts of mathematics and its applications that use the struc- ture of translations and modulations (or time-frequency shifts) for the anal- ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym- metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen- tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita- tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori- entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.

2,626 citations

Book
01 Jan 1962
TL;DR: In this paper, the basic theorem of Fourier analysis on ordered groups has been studied, and the structure of locally compact Abelian groups has also been studied in the context of topology.
Abstract: The Basic Theorems of Fourier Analysis. The Structure of Locally Compact Abelian Groups. Idempotent Measures. Homomorphisms of Group Algebras. Measures and Fourier Transforms on Thin Sets. Functions of Fourier Transforms. Closed Ideals in L 1 (G). Fourier Analysis on Ordered Groups. Closed Subalgebras of L 1 (G). Appendices: Topology, Topological Groups, Banach Spaces, Banach Algebras, Measure Theory. Bibliography. List of Special Symbols. Index.

2,443 citations

Journal ArticleDOI
TL;DR: In this paper, a set of MATLAB programs have been written to perform classical harmonic analysis for periods of about 1 year or shorter, account for unresolved constituents using nodal corrections, and compute confidence intervals for the analyzed components.

2,403 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023149
2022447
2021398
2020397
2019479
2018607