A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

Introduction of C Programming for DSP Applications

Multirate Filter Banks

Wavelet Filter Banks

Geometric Signal Theory

**Search Spectral Audio Signal Processing**

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In general, signals can be expanded as a linear combination
of *orthonormal basis signals* [248]. In the
discrete-time case, this can be expressed as

where the coefficient of projection of onto is given by

A set of signals
is said to be
a *biorthogonal basis set* if any signal can be represented
as

The following examples illustrate the Hilbert space point of view for various familiar cases of the Fourier transform and STFT. A more detailed introduction appears in Book I [248].

- Natural Basis
- Normalized DFT Basis for
- Normalized Fourier Transform Basis
- Normalized DTFT Basis
- Normalized STFT Basis
- Continuous Wavelet Transform
- Discrete Wavelet Transform
- Discrete Wavelet Filterbank
- Dyadic Filter Banks
- Dyadic Filter Bank Design
- Generalized STFT

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 http://ccrma.stanford.edu/~jos/ for details.

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