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The Discrete Fourier Transform, Part 2: Radix 2 FFT

Douglas Lyon


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This paper is part 2 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on a fast implementation of the DFT, called the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). The implementation is based on a well-known algorithm, called the Radix 2 FFT, and requires that its’ input data be an integral power of two in length.

Part 3 of this series of papers, demonstrates the computation of the PSD (Power Spectral Density) and applications of the DFT and IDFT. The applications include filtering, windowing, pitch shifting and the spectral analysis of re-sampling.

Note: Due to the typographical sophistication of this article, no HTML version is available. Please use the PDF version.

About the author

  Douglas A. Lyon (M'89-SM'00) received the Ph.D., M.S. and B.S. degrees in computer and systems engineering from Rensselaer Polytechnic Institute (1991, 1985 and 1983). Dr. Lyon has worked at AT&T Bell Laboratories at Murray Hill, NJ and the Jet Propulsion Laboratory at the California Institute of Technology, Pasadena, CA. He is currently the Chairman of the Computer Engineering Department at Fairfield University, in Fairfield CT, a senior member of the IEEE and President of DocJava, Inc., a consulting firm in Connecticut. Dr. Lyon has authored or co-authored three books (Java, Digital Signal Processing, Image Processing in Java and Java for Programmers). He has authored over 40 journal publications. Email: Web:

Douglas A. Lyon: "The Discrete Fourier Transform, Part 2: Radix 2 FFT", in Journal of Object Technology, vol. 8. no. 5, July-August 2009 pp. 21-33

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