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About: Spectrum Analysis Using the Discrete Fourier Transform

Module by: Douglas L. Jones. E-mail the author

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Name: Spectrum Analysis Using the Discrete Fourier Transform
ID: m12032
Language: English (en)
Summary: The discrete Fourier transform (DFT) maps a finite number of discrete time-domain samples to the same number of discrete Fourier-domain samples. Being practical to compute, it is the primary transform applied to real-world sampled data in digital signal processing. The DFT has special relationships with the discrete-time Fourier transform and the continuous-time Fourier transform that let it be used as a practical approximation of them through truncation and windowing of an infinite-length signal. Different window functions make various tradeoffs in the spectral distortions and artifacts introduced by DFT-based spectrum analysis.
Subject: Science and Technology
Keywords: DFT, DTFT, Fourier, IDFT
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 1.0
Authors: Douglas L. Jones (dl-jones@uiuc.edu)
Copyright Holders: Douglas L. Jones (dl-jones@uiuc.edu)
Maintainers: Douglas L. Jones (dl-jones@uiuc.edu), Kyle Clarkson (kclarks@gmail.com)
Latest version: 1.6 (history)
First publication date: May 11, 2004 3:47 pm GMT-5
Last revision to module: Sep 7, 2006 2:10 pm GMT-5
Module XML: m12032_1.6.cnxml

Version History

Version: 1.6 Sep 7, 2006 2:10 pm GMT-5 by Douglas L. Jones
Changes: 
Added example.
Added link targets.
Version: 1.5 Sep 2, 2006 10:09 pm GMT-5 by Douglas L. Jones
Changes: 
Greatly extended text.
Added discussion of window-based spectrum analysis and the tradeoffs between various windows.
Version: 1.4 Aug 29, 2006 10:22 pm GMT-5 by Douglas L. Jones
Changes: 
Extended text to add more explanation.
Added relation of DFT of a finite-length data block to DTFT samples.
Added explicit discussion of relation between DFT frequencies and analog FT.
Added solution to problem.
Fixed typographical errors.
Version: 1.3 Jun 18, 2004 10:41 am GMT-5 by Kyle Clarkson
Changes: 
Fixed Links
Version: 1.2 Jun 18, 2004 10:36 am GMT-5 by Kyle Clarkson
Changes: 
Added links and cnxns
Version: 1.1 Jun 7, 2004 4:05 pm GMT-5 by Kyle Clarkson
Changes: 
First Submission

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American Chemical Society (ACS) Style Guide:

Jones, D. Spectrum Analysis Using the Discrete Fourier Transform, Connexions Web site. http://cnx.org/content/m12032/1.6/, Sep 7, 2006.

American Medical Assocation (AMA) Manual of Style:

Jones D. Spectrum Analysis Using the Discrete Fourier Transform [Connexions Web site]. September 7, 2006. Available at: http://cnx.org/content/m12032/1.6/.

American Psychological Assocation (APA) Publication Manual:

Jones, D. (2006, September 7). Spectrum Analysis Using the Discrete Fourier Transform. Retrieved from the Connexions Web site: http://cnx.org/content/m12032/1.6/

Chicago Manual of Style (Bibliography):

Jones, Douglas. "Spectrum Analysis Using the Discrete Fourier Transform." Connexions. September 7, 2006. http://cnx.org/content/m12032/1.6/.

Chicago Manual of Style (Note):

Douglas Jones, "Spectrum Analysis Using the Discrete Fourier Transform," Connexions, September 7, 2006, http://cnx.org/content/m12032/1.6/.

Chicago Manual of Style (Reference, in Author-Date style):

Jones, D. 2006. Spectrum Analysis Using the Discrete Fourier Transform. Connexions, September 7, 2006. http://cnx.org/content/m12032/1.6/.

Modern Languages Association (MLA) Style Manual:

Jones, Douglas. Spectrum Analysis Using the Discrete Fourier Transform. Connexions. 7 Sep. 2006 <http://cnx.org/content/m12032/1.6/>.