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Example Applications of the DFT

This chapter gives a start on some applications of the DFT. First, we work through a progressive series of spectrum analysis examples using an efficient implementation of the DFT in Matlab or Octave. The various Fourier theorems provide a ``thinking vocabulary'' for understanding elements of spectral analysis. Next, the basics of linear systems theory are presented, relying heavily on the convolution theorem and properties of complex numbers. Finally, some applications of the DFT in statistical signal processing are introduced, including cross-correlation, matched filtering, system identification, power spectrum estimation, and coherence function measurement. A side topic in this chapter is practical usage of matlab for signal processing, including display of signals and spectra.

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About the Author: 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 (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 for details.


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