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WFILT_DB - Daubechies FIR filterbank

Usage

[h, g, a, info] = wfilt_db(N, compat = 1);

Input parameters

N Order of Daubechies filters.
compat 0 is precomputed LUT for \(N <= 38\), 1 is runtime calculation (default).

Output parameters

H cell array of analysing filters impulse reponses
G cell array of synthetizing filters impulse reponses
a array of subsampling (or hop) factors accociated with corresponding filters
info info.istight=1 indicates the wavelet system is a can. tight frame

Description

[H, G] = wfilt_db(N) computes a two-channel Daubechies FIR filterbank from prototype maximum-phase analysing lowpass filter obtained by spectral factorization of the Lagrange interpolator filter. N also denotes the number of zeros at \(z = -1\) of the lowpass filters of length \(2N\). The prototype lowpass filter has the following form (all roots of \(R(z)\) are inside of the unit circle):

\begin{equation*} H_l(z) = \left( 1 + z^{-1} \right)^N R(z), \end{equation*}

where \(R(z)\) is a spectral factor of the Lagrange interpolator \(P(z) = 2 R(z) * R(z^{-1})\) All subsequent filters of the two-channel filterbank are derived as follows:

\begin{equation*} H_h(z) = H_l((-z)^{-1}) \end{equation*}
\begin{equation*} G_l(z) = H_l(z^{-1}) \end{equation*}
\begin{equation*} G_h(z) = -H_l(-z) \end{equation*}

making them an orthogonal perfect-reconstruction QMF.

Examples:

wfiltinfo('db8');

References:

I. Daubechies. Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1992.