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Spectrum Analyzer: Introduction to Fast Fourier Transform

Module by: Douglas L. Jones, Swaroop Appadwedula, Matthew Berry, Mark Haun, Jake Janovetz, Michael Kramer, Dima Moussa, Daniel Sachs, Brian Wade. E-mail the authors

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Summary: The Fast Fourier transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform. The FFT is a block-based algorithm.

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Introduction

The Fast Fourier Transform (FFT) can be used to analyze the spectral content of a signal. Recall that the FFT is an efficient algorithm for computing the Discrete Fourier Transform (DFT), a frequency-sampled version of the DTFT.

DFT

Xk=∑n=0N−1xnⅇ-ⅈ2πNnk X k n 0 N 1 x n 2 N n k (1)
where n∧k∈01…N−1 n k 0 1 … N 1

Because the FFT is a block-based algorithm, its computation is performed at the block I/O rate, in contrast to other exercises in which processing occurred on a sample-by-sample basis.

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