Connexions

Sections
You are here: Home » Content » Spectrum Analysis Using the Discrete Fourier Transform

About: Spectrum Analysis Using the Discrete Fourier Transform

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

View the content: Spectrum Analysis Using the Discrete Fourier Transform

Metadata

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 -0500
Last revision to module: Sep 7, 2006 2:10 pm -0500

Downloads

PDF: m12032_1.6.pdf PDF file, for viewing content offline and printing. Learn more.
EPUB: m12032_1.6.epub Electronic publication file, for viewing in handheld devices. Learn more.
XML: m12032_1.6.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.
Source Export ZIP: m12032_1.6.zip ZIP containing the module XML plus any included media files. Can be reimported in the editing interface. Learn more.
Offline ZIP: m12032_1.6_offline.zip An offline HTML copy of the content. Also includes XML, included media files, and other support files. Learn more.

Version History

Version: 1.6 Sep 7, 2006 2:10 pm -0500 by Douglas L. Jones
Changes: 
Added example.
Added link targets.
Version: 1.5 Sep 2, 2006 10:09 pm -0500 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 -0500 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 -0500 by Kyle Clarkson
Changes: 
Fixed Links
Version: 1.2 Jun 18, 2004 10:36 am -0500 by Kyle Clarkson
Changes: 
Added links and cnxns
Version: 1.1 Jun 7, 2004 4:05 pm -0500 by Kyle Clarkson
Changes: 
First Submission

How to Reuse and Attribute This Content

If you derive a copy of this content using a Connexions account and publish your version, proper attribution of the original work will be automatically done for you.

If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 1.0), you must include

  • the authors' names: Douglas Jones
  • the title of the work: Spectrum Analysis Using the Discrete Fourier Transform
  • the Connexions URL where the work can be found: http://cnx.org/content/m12032/1.6/

See the citation section below for examples you can copy.

How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 1.0) of this work:

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/>.