Mixed-Radix Cooley-Tukey FFT

When the desired DFT length can be expressed as a product of smaller integers, the Cooley-Tukey decomposition provides what is called a mixed radix Cooley-Tukey FFT algorithm.^A.2

Two basic varieties of Cooley-Tukey FFT are decimation in time (DIT) and its Fourier dual, decimation in frequency (DIF). The next section illustrates decimation in time.

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Subsections

• Decimation in Time
• Radix 2 FFT
  • Radix 2 FFT Complexity is N Log N

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Order a Hardcopy of Mathematics of the DFT

Previous: Fast Fourier Transform (FFT) Algorithms
Next: Decimation in Time

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.