dtfilters
Analysis and synthesis filters for oversampled wavelet filter banks
Description
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 = 1.3678e-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 = 2.3803e-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 ofdtfilters
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 ofdtfilters
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.
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