idddtree

Inverse dual-tree and double-density 1-D wavelet transform

Syntax

xrec = idddtree(wt)

Description

xrec = idddtree(wt) returns the inverse wavelet transform of the wavelet decomposition (analysis filter bank), wt. wt is the output of dddtree.

Examples

Perfect Reconstruction Using Dual-Tree Double-Density Wavelet Filter Bank

Demonstrate perfect reconstruction of a signal using a dual-tree double-density wavelet transform.

Load the noisy Doppler signal. Obtain the dual-tree double-density wavelet transform down to level 5. Invert the transform and demonstrate perfect reconstruction.

load noisdopp;
wt = dddtree('cplxdddt',noisdopp,5,'FSdoubledualfilt',...
     'doubledualfilt');
xrec = idddtree(wt);
max(abs(noisdopp-xrec))

ans = 
1.9291e-12

Input Arguments

wt — Wavelet transform

structure

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

type — Type of wavelet decomposition (filter bank)

'dwt' | 'ddt' | 'cplxdt' | 'cplxdddt'

Type of wavelet decomposition (filter bank), specified as one of 'dwt', 'ddt', 'cplxdt', or 'cplxdddt'. The type,'dwt', gives a critically sampled discrete wavelet transform. The other types are oversampled wavelet transforms. 'ddt' is a double-density wavelet transform, 'cplxdt' is a dual-tree complex wavelet transform, and 'cplxdddt' is a double-density dual-tree complex wavelet transform.

level — Level of wavelet decomposition

positive integer

Level of 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-stage analysis filters, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 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 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 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 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 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 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.

• 'cplxdddt' — cfs{j}(:,:,k,m)

  • j = 1,2 level is the level.

  • k = 1,2 is the wavelet filter.

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

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

Output Arguments

xrec — Synthesized 1-D signal

vector

Synthesized 1-D signal, returned as a vector. The row or column orientation of xrec depends on the row or column orientation of the 1-D signal input to dddtree.

Data Types: double

Version History

Introduced in R2013b