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See Also

Embedded SystemsFPGAElectronics

Spectral Audio Signal Processing
    FIR Digital Filter Design
       Optimal FIR Digital Filter Design
          Least-Squares Linear-Phase FIR Filter Design
             Matrix Formulation: Optimal Design, Cont'd

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Matrix Formulation: Optimal Design, Cont'd

In matrix notation, our filter design problem can be stated

$\displaystyle \min_x \left\Vert Ax-b \right\Vert _2^2 $

where

$\displaystyle A \mathrel{\stackrel{\Delta}{=}}\left[ \begin{array}{ccccc} 1 & 2... ...a_{N-1}) & \dots & 2\cos\left[\omega_{N-1}(L-1)\right] \\ \end{array} \right] $

$\displaystyle x \mathrel{\stackrel{\Delta}{=}}h $

and $ b=[D(\omega_k)]$ is the desired frequency response at the specified frequencies.

Previous: Least-Squares Linear-Phase FIR Filter Design
Next: Least Squares Optimization

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About the Author: 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.


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