idddtree
Inverse dual-tree and double-density 1-D wavelet transform
Syntax
Description
Examples
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
Wavelet transform, returned as a structure from dddtree
with these fields:
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 of wavelet decomposition, specified as a positive integer.
Decomposition (analysis) and reconstruction (synthesis) filters, specified as a structure with these fields:
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.
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.
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.
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.
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
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
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