First-level dual-tree biorthogonal filters
Obtain the decomposition and reconstruction filters associated with the biorthogonal wavelet
fname = 'nearsym5_7'; [LoD,HiD,LoR,HiR] = qbiorthfilt(fname);
dwtfilterbank function to create a 7-level discrete wavelet transform filter bank with the biorthogonal filters. Specify the wavelet filter type as
analysis. Because the filters are not of even lengths, extend the filters appropriately to match powers of their z-transforms.
scal(:,1) = [0 0 LoD' 0]; scal(:,2) = [0 LoR']; wavf(:,1) = [0 HiD']; wavf(:,2) = [0 0 HiR' 0]; fb = dwtfilterbank('Wavelet','Custom',... 'CustomScalingFilter',scal,... 'CustomWaveletFilter',wavf,... 'Level',7,... 'FilterType','analysis');
Obtain the time-domain wavelets corresponding to the wavelet passband filters. Plot the coarsest-scale wavelet.
[psi,t] = wavelets(fb); plot(t,psi(end,:)) grid on xlabel('Time') ylabel('Amplitude')
name— First-level biorthogonal filter
First-level biorthogonal filter used in Kingsbury's Q-shift complex dual-tree transform, specified by one of the values listed here.
 Antonini, M., M. Barlaud, P. Mathieu, and I. Daubechies. “Image Coding Using Wavelet Transform.” IEEE Transactions on Image Processing 1, no. 2 (April 1992): 205–20. https://doi.org/10.1109/83.136597.
 Kingsbury, Nick. “Complex Wavelets for Shift Invariant Analysis and Filtering of Signals.” Applied and Computational Harmonic Analysis 10, no. 3 (May 2001): 234–53. https://doi.org/10.1006/acha.2000.0343.
 Le Gall, D., and A. Tabatabai. “Sub-Band Coding of Digital Images Using Symmetric Short Kernel Filters and Arithmetic Coding Techniques.” In ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 761–64. New York, NY, USA: IEEE, 1988. https://doi.org/10.1109/ICASSP.1988.196696.