DFT Math Outline

In summary, understanding the DFT takes us through the following topics:

• Complex numbers
• Complex exponents
• Why ?
• Euler's identity
• Projecting signals onto signals via the inner product
• The DFT as the coefficient of projection of a signal onto a sinusoid
• The IDFT as a sum of projections onto sinusoids
• Various Fourier theorems
• Elementary time-frequency pairs
• Practical spectrum analysis in matlab

We will additionally discuss various practical aspects of working with signals and spectra.

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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.