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

Digital Waveguide Theory

Alternative Wave Variables

Root-Power Waves

**Search Physical Audio Signal Processing**

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It is sometimes helpful to *normalize* the wave variables so that
signal power is uniformly distributed numerically. This can be especially
helpful in fixed-point implementations.

From (C.49), it is clear that power normalization is given by

where we have dropped the common time argument `' for simplicity. As a result, we obtain

and

The normalized wave variables and behave physically like force and velocity waves, respectively, but they are scaled such that either can be squared to obtain instantaneous signal power. Waveguide networks built using normalized waves have many desirable properties [174,172,432]. One is the obvious numerical advantage of uniformly distributing signal power across available dynamic range in fixed-point implementations. Another is that only in the normalized case can the wave impedances be made

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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