plotdt

Plot dual-tree or double-density wavelet transform

Syntax

plotdt(wt)

Description

plotdt(wt) plots the coefficients of the 1-D or 2-D wavelet filter bank decomposition, wt.

Examples

Plot Complex Dual-Tree Wavelet Transform of 1-D Signal

Plot the complex dual-tree wavelet transform of the noisy Doppler signal.

Load the noisy Doppler signal. Obtain the complex dual-tree wavelet transform down to level 4.

load noisdopp;
wt = dddtree('cplxdt',noisdopp,4,'dtf1');

Plot the coefficients.

plotdt(wt)

Plot Complex Oriented Dual-Tree Wavelet Transform of 2-D Image

Plot the complex oriented dual-tree wavelet transform of an image.

Load the xbox image. Obtain the complex oriented dual-tree wavelet transform down to level 3.

load xbox;
wt = dddtree2('cplxdt',xbox,3,'dtf1');

Plot the coefficients.

plotdt(wt)

Select the desired level detail coefficients from the drop-down list.

Input Arguments

wt — Wavelet transform

structure

Wavelet transform, returned as a structure from dddtree or dddtree2 with these fields:

type — Type of wavelet decomposition (filter bank)

'dwt' | 'ddt' | 'realdt' | 'cplxdt' | 'realdddt' | 'cplxdddt'

Type of wavelet decomposition (filter bank), specified as one of 'dwt', 'ddt', 'realdt', 'cplxdt',, 'realdddt', or 'cplxdddt'. 'realdt' and 'realdddt' are only valid for the 2-D wavelet transform. The type, 'dwt', is a critically sampled (nonredundant) discrete wavelet transform for 1-D data or 2-D images. The other decomposition types are oversampled wavelet transforms. For details about transform types see dddtree for 1-D wavelet transforms and dddtree2 for 2-D wavelet transforms.

level — Level of the wavelet decomposition

positive integer

Level of the wavelet decomposition, specified as a positive integer.

filters — Decomposition (analysis) and reconstruction (synthesis) filters

structure

Decomposition (analysis) and reconstruction (synthesis) filters, specified as a structure with these fields:

Fdf — First-stage analysis filters

matrix | cell array

First level decomposition filters specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the first-stage analysis filters for the corresponding tree.

Df — Analysis filters for levels > 1

matrix | cell array

Analysis filters for levels > 1, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the analysis filters for the corresponding tree.

Frf — First-level reconstruction filters

matrix | cell array

First-level reconstruction filters, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the first-stage synthesis filters for the corresponding tree.

Rf — Reconstruction filters for levels > 1

matrix | cell array

Reconstruction filters for levels > 1, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the first-stage synthesis filters for the corresponding tree.

cfs — Wavelet transform coefficients

cell array of matrices

Wavelet transform coefficients, specified as a 1-by-(level+1) cell array of matrices. The size and structure of the matrix elements of the cell array depend on the type of wavelet transform and whether the decomposition is 1-D or 2-D. For a 1-D wavelet transform, the coefficients are organized by transform type as follows:

• 'dwt' — cfs{j}

  • j = 1,2,...level is the level.

  • cfs{level+1} are the lowpass, or scaling, coefficients.

• 'ddt' — cfs{j}(:,:,k)

  • j = 1,2,... level is the level.

  • k = 1,2 is the wavelet filter.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'cplxdt' — cfs{j}(:,:,m)

  • j = 1,2,... level is the level.

  • m = 1,2 are the real and imaginary parts.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'realdddt' — cfs{j}(:,:,d,k)

  • j = 1,2,... level is the level.

  • d = 1,2,3 is the orientation.

  • k = 1,2 is the wavelet transform tree.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'cplxdddt' — cfs{j}(:,:,d,k,m)

  • j = 1,2,... level is the level.

  • k = 1,2 is the wavelet transform tree.

  • m = 1,2 are the real and imaginary parts.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

For a 2-D wavelet transform, the coefficients are organized by transform type as follows:

• 'dwt' — cfs{j}(:,:,d)

  • j = 1,2,... level is the level.

  • d = 1,2,3 is the orientation.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'ddt' — cfs{j}(:,:,d)

  • j = 1,2,... level is the level.

  • d = 1,2,3,4,5,6,7,8 is the orientation.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'realddt' — cfs{j}(:,:,d,k)

  • j = 1,2,... level is the level.

  • d = 1,2,3 is the orientation.

  • k = 1,2 is the wavelet transform tree.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'cplxdt' — cfs{j}(:,:,d,k,m)

  • j = 1,2,... level is the level.

  • d = 1,2,3 is the orientation.

  • k = 1,2 is the wavelet transform tree.

  • m = 1,2 are the real and imaginary parts.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'realdddt' — cfs{j}(:,:,d,k)

  • j = 1,2,... level is the level.

  • d = 1,2,3 is the orientation.

  • k = 1,2 is the wavelet transform tree.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

• 'cplxdddt' — cfs{j}(:,:,d,k,m)

  • j = 1,2,... level is the level.

  • d = 1,2,3 is the orientation.

  • k = 1,2 is the wavelet transform tree.

  • m = 1,2 are the real and imaginary parts.

  • cfs{level+1}(:,:) are the lowpass, or scaling, coefficients.

Version History

Introduced in R2013b