DTWFBREAL - Dual-Tree Wavelet FilterBank for real-valued signals

Usage

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

Input parameters

Output parameters

Description

c=dtwfbtreal(f,dualwt) computes dual-tree complex wavelet coefficients of the real-valued signal f. The representation is approximately time-invariant and provides analytic behavior. 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 filterbanks, but one half of the coefficients is complex conjugate of the other.

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 increasing subband center frequency.

In addition, the function returns struct. info containing transform parameters. It can be conviniently used for the inverse transform idtwfbreal e.g. fhat = idtwfbreal(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 filterbank 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 filterbank to achieve the half-sample shift ultimatelly resulting in analytic (complex) behavior of the transform.

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

   Different filterbank 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 filterbank.

   'full'

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

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

   The filterbank is designed such that it mimics 4-band, 8-band or 16-band complex wavelet transform provided the basic filterbank 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 filterbank can use any basic wavelet filterbank in the first stage of both trees, provided they are shifted by 1 sample (done internally). A custom first stage filterbank can be defined by passing the following key-value pair in the cell array:

   'first',`w`

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

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

   'leaf',`w`

   w defines a regular basic filterbank. 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 filterbank tree without modifications. The ordering differ 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 dtwfbreal function using the regular DWT iterated filterbank. The second figure shows a magnitude frequency response of an identical filterbank.:

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

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

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