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Normalized DTFT Basis

The Discrete Time Fourier Transform (DTFT) is similar to the Fourier transform case:

$\displaystyle \varphi _\omega (n) \isdef e^{j\omega n}/\sqrt{2\pi},\quad \omega \in (-\pi,\pi], \quad n\in (-\infty,\infty)$ (12.114)

The inner product $ \left<\varphi _\omega ,x\right>$ and reconstruction of $ x(n)$ in terms of $ \{\varphi _\omega \}$ are left as exercises.


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA