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About: Decimation-in-Frequency (DIF) Radix-2 FFT

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

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Name: Decimation-in-Frequency (DIF) Radix-2 FFT
ID: m12018
Language: English (en)
Summary: The radix-2 algorithms are the simplest FFT algorithms. The decimation-in-frequency (DIF) radix-2 FFT partitions the DFT computation into even-indexed and odd-indexed outputs, which can each be computed by shorter-length DFTs of different combinations of input samples. Recursive application of this decomposition to the shorter-length DFTs results in the full radix-2 decimation-in-frequency FFT.
Subject: Science and Technology
Keywords: Cooley-Tukey, decimation in frequency, fast Fourier transform, FFT, radix-2, twiddle factor
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 1.0

Authors: Douglas L. Jones (
Copyright Holders: Douglas L. Jones (
Maintainers: Douglas L. Jones (, Harika Basana (, Kyle Clarkson (

Latest version: 1.6 (history)
First publication date: May 17, 2004 3:59 pm -0500
Last revision to module: Sep 17, 2006 8:47 am -0500


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Version History

Version: 1.6 Sep 17, 2006 8:47 am -0500 by Douglas L. Jones
Added a lot of text.
Fixed typos and equation errors.
Added many links in text.

Version: 1.5 Jul 23, 2004 11:35 am -0500 by Kyle Clarkson
Added .eps versions of images

Version: 1.4 Jun 21, 2004 2:32 pm -0500 by Kyle Clarkson
Fixed Typo in Title

Version: 1.3 Jun 18, 2004 3:08 pm -0500 by Kyle Clarkson
Added cnxns and links

Version: 1.2 Jun 17, 2004 2:03 pm -0500 by Kyle Clarkson
changed images to pngs

Version: 1.1 Jun 7, 2004 3:57 pm -0500 by Kyle Clarkson
First Submission

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Jones, D. Decimation-in-Frequency (DIF) Radix-2 FFT, OpenStax-CNX Web site., Sep 17, 2006.

American Medical Assocation (AMA) Manual of Style:

Jones D. Decimation-in-Frequency (DIF) Radix-2 FFT [OpenStax-CNX Web site]. September 17, 2006. Available at:

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Jones, D. (2006, September 17). Decimation-in-Frequency (DIF) Radix-2 FFT. Retrieved from the OpenStax-CNX Web site:

Chicago Manual of Style (Bibliography):

Jones, Douglas. "Decimation-in-Frequency (DIF) Radix-2 FFT." OpenStax-CNX. September 17, 2006.

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Douglas Jones, "Decimation-in-Frequency (DIF) Radix-2 FFT," OpenStax-CNX, September 17, 2006,

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Jones, D. 2006. Decimation-in-Frequency (DIF) Radix-2 FFT. OpenStax-CNX, September 17, 2006.

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Jones, Douglas. Decimation-in-Frequency (DIF) Radix-2 FFT. OpenStax-CNX. 17 Sep. 2006 <>.