hanscalf
Han real orthogonal scaling filters with sum and linear-phase moments
Since R2022b
Syntax
Description
Examples
Han Real Orthogonal Wavelet
Obtain the scaling filter corresponding to the Han real orthogonal wavelet with five sum rules and five linear-phase moments.
scalf = hanscalf("han5.5");
Use orthfilt
to obtain the scaling and wavelet filters corresponding to the wavelet.
[LoD,HiD,LoR,HiR] = orthfilt(scalf);
Confirm the filters form an orthonormal perfect reconstruction wavelet filter bank.
[tf,checks] = isorthwfb(LoD)
tf = logical
1
checks=7×3 table
Pass-Fail Maximum Error Test Tolerance
_________ _____________ ______________
Equal-length filters pass 0 0
Even-length filters pass 0 0
Unit-norm filters pass 1.2168e-13 1.4901e-08
Filter sums pass 2.1645e-13 1.4901e-08
Even and odd downsampled sums pass 1.0836e-13 1.4901e-08
Zero autocorrelation at even lags pass 1.2484e-13 1.4901e-08
Zero crosscorrelation at even lags pass 2.1922e-17 1.4901e-08
Create two discrete wavelet transform filter banks, one using the Han wavelet, and the other using the Haar wavelet. Specify a single level of decomposition for both filter banks. Plot the one-sided magnitude frequency responses of both filter banks. The Han wavelet has a larger frequency separation between the wavelet and scaling filters than the Haar wavelet.
fbHan = dwtfilterbank(Wavelet="han5.5",Level=1); fbHaar = dwtfilterbank(Wavelet="haar",Level=1); freqz(fbHan)
figure freqz(fbHaar)
Input Arguments
wname
— Han scaling filter
"hanSR.LP"
Han scaling filter, specified as
"hanSR.LP"
, where
SR is the number of sum rules, and LP is the
number of linear-phase moments. wname
can be
"han2.3"
, "han3.3"
, "han4.5"
,
or "han5.5"
. For information on the filter properties, see Han Real Orthogonal Scaling Filters.
Output Arguments
More About
Han Real Orthogonal Scaling Filters
Han filters are characterized by their order of sum rules, linear-phase
moments, and phase. This table lists the filter specifications for the valid values of
wname
.
wname | Order of Sum Rules | Number of Linear-Phase Moments | Normalized Variance of Filter Impulse Response | Frequency Separation Between Scaling and Wavelet Filter | Length |
---|---|---|---|---|---|
"han2.3"
| 2 | 3 | 0.465 | 0.8156 | 6 |
"han2.3" | 2 | 3 | 0.426 | 0.8540 | 8 |
"han4.5" | 4 | 5 | 0.488 | 0.8563 | 10 |
"han5.5" | 5 | 5 | 0.530 | 0.8867 | 14 |
Frequency separation is a number between 0 and 1, where 0 indicates the filters are
perfectly matched and 1 indicates they are perfectly separated in frequency. As a point of
reference, the Haar ("db1"
) wavelet filter has the smallest normalized
variance of all wavelet filters with 0.25 and poorest frequency separation with 0.666. An
example of a scaling and wavelet filter pair with a relatively large frequency separation is
the Fejér-Korovkin ("fk22"
) 22-coefficient filter with a value of
0.9522.
References
[1] Han, Bin. “Wavelet Filter Banks.” In Framelets and Wavelets: Algorithms, Analysis, and Applications, 92–98. Applied and Numerical Harmonic Analysis. Cham, Switzerland: Birkhäuser, 2017. https://doi.org/10.1007/978-3-319-68530-4_2.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2022b
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