Thread View: sci.math.num-analysis
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Started by Surya N Kavuri
Sun, 06 Sep 1992 18:14
Fourier series approximation
Author: Surya N Kavuri
Date: Sun, 06 Sep 1992 18:14
Date: Sun, 06 Sep 1992 18:14
4 lines
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When the data is NOT sampled at regular intervals, how are the fourier coefficients determined ? Surya
Re: Fourier series approximation
Author: David Steinman
Date: Sun, 06 Sep 1992 20:50
Date: Sun, 06 Sep 1992 20:50
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kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes: > When the data is NOT sampled at regular intervals, how are the fourier > coefficients determined ? Well, it may not be pretty (or even that accurate), but I usually just integrate the coefficient integrals using a trapezoidal rule. -- Dave!
Re: Fourier series approximation
Author: Richard Harter
Date: Mon, 07 Sep 1992 05:25
Date: Mon, 07 Sep 1992 05:25
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In article <Bu6CKC.6tF@me.utoronto.ca> steinman@me.utoronto.ca (David Steinman) writes: >kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes: >> When the data is NOT sampled at regular intervals, how are the fourier >> coefficients determined ? >Well, it may not be pretty (or even that accurate), but I usually just >integrate the coefficient integrals using a trapezoidal rule. There are three cases of interest that I can think of: (a) The sampling is completely irregular. (b) The sampling is perturbed from periodic. (c) The sampling is a replication of a fixed irregular sample. Case (a) can be handled by a large least squares matrix, but is practically handled by integration. Case (b) can be handled by a linear perturbation technique. Case (c) can be handled by a least squares solution with the the irregular sample combined with standard equal interval fourier transform outside the interval. An example of case (c) is measurements taken during daylight hours at fixed times every day. Details are left as an exercise for the reader. -- Richard Harter: SMDS Inc. Net address: rh@smds.com Phone: 508-369-7398 US Mail: SMDS Inc., PO Box 555, Concord MA 01742. Fax: 508-369-8272 In the fields of Hell where the grass grows high Are the graves of dreams allowed to die.
Re: Fourier series approximation
Author: John W. Herman
Date: Tue, 08 Sep 1992 20:04
Date: Tue, 08 Sep 1992 20:04
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rh@smds.com (Richard Harter) writes: >In article <Bu6CKC.6tF@me.utoronto.ca> steinman@me.utoronto.ca (David Steinman) writes: >>kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes: >>> When the data is NOT sampled at regular intervals, how are the fourier >>> coefficients determined ? >>Well, it may not be pretty (or even that accurate), but I usually just >>integrate the coefficient integrals using a trapezoidal rule. >There are three cases of interest that I can think of: Look at the definition of the Discrete Fourier Transform. Before simplification, it contains the time as an explicit variable. Try this first with a finite length window (read finite number of samples).
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