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Variable parameter window families for digital spectral analysis

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TLDR
Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered and closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc.
Abstract
Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered. Closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc. Simple expressions relating to mainlobe width and maximum sidelobe level are given for the two families considered. The results are compared to those obtained by J.F. Kaiser and R.W. Schafer (1980) in the case of zeroth-order Bessel (I/sub 0/-sinh) family. >

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Design of Tight Minimum-Sidelobe Windows by Riemannian Newton's Method.

TL;DR: In this paper, a method of designing tight windows that minimize the sidelobe energy is proposed, which is formulated as an optimization problem on an oblique manifold, and a Riemannian Newton algorithm on this manifold is derived to efficiently obtain a solution.
References
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Journal ArticleDOI

An algorithm for the machine calculation of complex Fourier series

TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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On the use of windows for harmonic analysis with the discrete Fourier transform

F.J. Harris
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.
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Prolate spheroidal wave functions, fourier analysis and uncertainty — II

TL;DR: In this paper, the authors apply the theory developed in the preceding paper to a number of questions about timelimited and bandlimited signals, and find the signals which do the best job of simultaneous time and frequency concentration.
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Measurement and Analysis of Random Data

Edwin L. Crow
- 01 Nov 1968 - 
TL;DR: In this paper, Measurement and Analysis of Random Data (MADR) is used for the analysis of random data in the context of measurement and analysis of statistical data sets.
Journal ArticleDOI

Some windows with very good sidelobe behavior

TL;DR: Correct plots of Harris' windows are presented and additional windows with very good sidelobes and optimal behavior under several different constraints are derived.