DTWFB - Dual-Tree Wavelet Filter Bank

Usage

c=dtwfb(f,dualwt);
c=dtwfb(f,{dualw,J});
[c,info]=dtwfb(...);

Input parameters

Output parameters

Description

c=dtwfbt(f,dualwt) computes dual-tree complex wavelet coefficients of the signal f. The representation is approximately time-invariant and provides analytic behaviour. Due to these facts, the resulting subbands are nearly aliasing free making them suitable for severe coefficient modifications. The representation is two times redundant, provided critical subsampling of all involved filter banks.

The shape of the filterbank tree and filters used is controlled by dualwt (for possible formats see below). The output c is a cell-array with each element containing a single subband. The subbands are ordered with the increasing subband centre frequency.

In addition, the function returns struct. info containing transform parameters. It can be conveniently used for the inverse transform idtwfb e.g. fhat = idtwfb(c,info). It is also required by the plotwavelets function.

If f is a matrix, the transform is applied to each column.

Two formats of dualwt are accepted:

1. Cell array of parameters. First two elements of the array are mandatory {dualw,J}.

   dualw

   Basic dual-tree filters

   J

   Number of levels of the filter bank tree

   Possible formats of dualw are the same as in fwtinit except the wfiltdt_ prefix is used when searching for function specifying the actual impulse responses. These filters were designed specially for the dual-tree filter bank to achieve the half-sample shift ultimately resulting in analytic (complex) behaviour of the transform.

   The default shape of the filter bank tree is DWT i.e. only low-pass output is decomposed further (J times in total).

   Different filter bank tree shapes can be obtained by passing additional flag in the cell array. Supported flags (mutually exclusive) are:

   'dwt'

   Plain DWT tree (default). This gives one band per octave freq. resolution when using 2 channel basic wavelet filter bank.

   'full'

   Full filter bank tree. Both (all) basic filter bank outputs are decomposed further up to depth J achieving linear frequency band division.

   'doubleband',`'quadband','octaband'`

   The filter bank is designed such that it mimics 4-band, 8-band or 16-band complex wavelet transform provided the basic filter bank is 2 channel. In this case, J is treated such that it defines number of levels of 4-band, 8-band or 16-band transform.

   The dual-tree wavelet filter bank can use any basic wavelet filter bank in the first stage of both trees, provided they are shifted by 1 sample (done internally). A custom first stage filter bank can be defined by passing the following key-value pair in the cell array:

   'first',`w`

   w defines a regular basic filter bank. Accepted formats are the same as in fwtinit assuming the wfilt_ prefix.

   Similarly, when working with a filter bank tree containing decomposition of high-pass outputs, some filters in both trees must be replaced by a regular basic filter bank in order to achieve the approximately analytic behaviour. A custom filter bank can be specified by passing another key-value pair in the cell array:

   'leaf',`w`

   w defines a regular basic filter bank. Accepted formats are the same as in fwtinit assuming the wfilt_ prefix.

2. Another possibility is to pass directly a struct. returned by dtwfbinit and possibly modified by wfbtremove.

Optional args.:

In addition, the following flag groups are supported:

'freq',`'nat'`

Frequency or natural (Paley) ordering of coefficient subbands. By default, subbands are ordered according to frequency. The natural ordering is how the subbands are obtained from the filter bank tree without modifications. The ordering differs only in non-plain DWT case.

Boundary handling:

In contrast with fwt, wfbt and wpfbt, this function supports periodic boundary handling only.

Examples:

A simple example of calling the dtwfb function using the regular DWT iterated filter bank. The second figure shows a magnitude frequency response of an identical filter bank.:

[f,fs] = greasy;
J = 6;
[c,info] = dtwfb(f,{'qshift3',J});
figure(1);
plotwavelets(c,info,fs,'dynrange',90);
figure(2);
[g,a] = dtwfb2filterbank({'qshift3',J});
filterbankfreqz(g,a,1024,'plot','linabs');

The second example shows a decomposition using a full filter bank tree of depth J:

[f,fs] = greasy;
J = 5;
[c,info] = dtwfb(f,{'qshift4',J,'full'});
figure(1);
plotwavelets(c,info,fs,'dynrange',90);
figure(2);
[g,a] = dtwfb2filterbank({'qshift4',J,'full'});
filterbankfreqz(g,a,1024,'plot','linabs');