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Spectral Audio Signal Processing
Multirate Filter Banks
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Geometric Signal Theory
Normalized DTFT Basis
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Normalized DTFT Basis
The Discrete Time Fourier Transform (DTFT) is similar to the Fourier transform case:
![$\displaystyle \varphi _\omega (n) \isdef e^{j\omega n}/\sqrt{2\pi},\quad
\omega \in (-\pi,\pi], \quad
n\in (-\infty,\infty)
$](http://www.dsprelated.com/josimages_new/sasp/img2051.png){kind=small}
and reconstruction of 
in
terms of
are left as exercises.
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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.
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