dtfilters

Analysis and synthesis filters for oversampled wavelet filter banks

Syntax

df = dtfilters(name)

[df,rf] = dtfilters(name)

Description

df = dtfilters(name) returns the decomposition (analysis) filters corresponding to name. These filters are used most often as input arguments to dddtree and dddtree2.

[df,rf] = dtfilters(name) returns the reconstruction (synthesis) filters corresponding to name.

Examples

Filters for Complex Dual-Tree Wavelet Transform

Obtain valid filters for the complex dual-tree wavelet transform. The transform uses Farras nearly symmetric filters for the first stage and Kingsbury Q-shift filters with 10 taps for subsequent stages.

Load the noisy Doppler signal. Obtain the filters for the first and subsequent stages of the complex dual-tree wavelet transform. Demonstrate perfect reconstruction using the complex dual-tree wavelet transform.

load noisdopp;
df = dtfilters('dtf2');
dt = dddtree('cplxdt',noisdopp,5,df{1},df{2});
xrec = idddtree(dt);
max(abs(noisdopp-xrec))

ans = 1.3323e-13

Filters for Double-Density Wavelet Transform

Obtain valid filters for the double-density wavelet transform.

Load the noisy Doppler signal. Obtain the filters for the double-density wavelet transform. The double-density wavelet transform uses the same filters at all stages. Demonstrate perfect reconstruction using the double-density wavelet transform.

df = dtfilters('filters1');
load noisdopp;
dt = dddtree('ddt',noisdopp,5,df,df);
xrec = idddtree(dt);
max(abs(noisdopp-xrec))

ans = 2.3892e-13

Input Arguments

name — Filter name

'dtf1' | 'dddtf1' | 'self1' | 'self2' | ...

Filter name, specified as a character vector or string scalar. Valid entries for name are:

• Any valid orthogonal or biorthogonal wavelet name. See wfilters for details. An orthogonal or biorthogonal wavelet is only valid when the filter bank type is 'dwt', or when you use the filter as the first stage in a complex dual-tree transform, 'realdt' or 'cplxdt'. An orthogonal or biorthogonal wavelet filter is not a valid filter if you have a double-density, 'ddt' or dual-tree double-density, 'realdddt' or 'cplxdddt', filter bank. An orthogonal or biorthogonal wavelet filter is not a valid filter for complex dual-tree filter banks for stages greater than 1.

• 'dtfP' — With P equal to 1, 2, 3, 4, or 5 returns the first-stage Farras filters ('FSfarras') and Kingsbury Q-shift filters ('qshiftN') for subsequent stages. This input is only valid for a dual-tree transform, 'realdt' or 'cplxdt'. Setting P = 1, 2, 3, 4, or 5 specifies the Kingsbury Q-shift filters with N = 6, 10, 14, 16, or 18 taps, respectively.

• 'dddtf1' — Returns the filters for the first and subsequent stages of the double-density dual-tree transform. This input is only valid for the double-density dual-tree transforms, 'realdddt' and 'cplxdddt'.

• 'self1' — Returns 10-tap filters for the double-density wavelet transform. This option is only valid for double-density wavelet transforms, 'ddt', 'realdddt', and 'cplxdddt'.

• 'self2' — Returns 16-tap filters for the double-density wavelet transform. This option is only valid for double-density wavelet transforms, 'ddt', 'realdddt', and 'cplxdddt'.

• 'filters1' — Returns 6-tap filters for the double-density wavelet transform, 'ddt'.

• 'filters2' — Returns 12-tap filters for the double-density wavelet transform, 'ddt'.

• 'farras' — Farras nearly symmetric filters for a two-channel perfect reconstruction filter bank. This option is meant to be used for one-tree transforms and is valid only for an orthogonal critically sampled wavelet transform, 'dwt'. The output of dtfilters is a two-column matrix. The first column of the matrix is a scaling (lowpass) filter, and the second column is a wavelet (highpass) filter.

• 'FSfarras' — Farras nearly symmetric first-stage filters intended for a dual-tree wavelet transform. With this option, the output of dtfilters is a cell array with two elements, one for each tree. Each element is a two-column matrix. The first column of the matrix is a scaling (lowpass) filter, and the second column is a wavelet (highpass) filter.

• 'qshiftN' — Kingsbury Q-shift N-tap filters with N = 6, 10, 14, 16, or 18. The Kingsbury Q-shift filters are used most commonly in dual-tree wavelet transforms for stages greater than 1.

• 'doubledualfilt' — Filters for one stage of the double-density dual-tree wavelet transforms, 'realdddt' or 'cplxdddt'.

Output Arguments

df — Decomposition (analysis) filters

matrix | cell array

Decomposition (analysis) filters, returned as a matrix or cell array of matrices.

rf — Reconstruction (synthesis) filters

matrix | cell array

Reconstruction (synthesis) filters, returned as a matrix or cell array of matrices.