blscalf
Syntax
Description
Examples
Best-Localized Daubechies Wavelet
Obtain the scaling filter corresponding to the best-localized Daubechies wavelet with 10 vanishing moments. Confirm the sum of the filter coefficients nearly equals and the L2 norm of the filter nearly equals 1.
scalf = blscalf("bl10");
sum(scalf)-sqrt(2)
ans = -2.2204e-16
norm(scalf,2)
ans = 1.0000
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 1.7665e-10 1.4901e-08
Filter sums pass 7.2923e-15 1.4901e-08
Even and odd downsampled sums pass 3.7748e-15 1.4901e-08
Zero autocorrelation at even lags pass 7.3088e-11 1.4901e-08
Zero crosscorrelation at even lags pass 1.3089e-17 1.4901e-08
Create a discrete wavelet transform filter bank using the wavelet. Plot the frequency responses of the wavelet filters and the final resolution scaling filter for the default signal length.
fb = dwtfilterbank(Wavelet="bl10");
freqz(fb)
Plot the wavelet at the coarsest scale.
[psi,t] = wavelets(fb); plot(t,psi(end,:)) grid on title("Wavelet")
Plot the scaling function at the coarsest scale.
[phi,t] = scalingfunctions(fb); plot(t,phi(end,:)) grid on title("Scaling Function")
Input Arguments
wname
— Best-localized Daubechies wavelet
"bl7"
| "bl9"
| "bl10"
Best-localized Daubechies wavelet, specified as one of these:
"bl7"
— Best-localized Daubechies wavelet with seven vanishing moments"bl9"
— Best-localized Daubechies wavelet with nine vanishing moments"bl10"
— Best-localized Daubechies wavelet with 10 vanishing moments
Output Arguments
scalf
— Scaling filter
vector
Scaling filter corresponding to wname
, returned as a vector.
scalf
should be used in conjunction with orthfilt
to obtain scaling and wavelet filters with the proper
normalization. The scaling filters agree exactly with Doroslovački [1]. The sum of filter
coefficients is nearly √2 and the L2 norm is nearly 1.0.
Data Types: double
References
[1] Doroslovački, M.L. “On the Least Asymmetric Wavelets.” IEEE Transactions on Signal Processing 46, no. 4 (April 1998): 1125–30. https://doi.org/10.1109/78.668562.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2022b
MATLAB 명령
다음 MATLAB 명령에 해당하는 링크를 클릭했습니다.
명령을 실행하려면 MATLAB 명령 창에 입력하십시오. 웹 브라우저는 MATLAB 명령을 지원하지 않습니다.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)