Best-localized Daubechies scaling filter
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
ans = 1.0000
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")
wname — Best-localized Daubechies wavelet
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
scalf — Scaling filter
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 . The sum of filter
coefficients is nearly √2 and the L2 norm is nearly 1.0.
 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.
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Introduced in R2022b