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# qbiorthfilt

First-level dual-tree biorthogonal filters

Since R2020a

## Syntax

``[LoD,HiD,LoR,HiR] = qbiorthfilt(name)``

## Description

example

````[LoD,HiD,LoR,HiR] = qbiorthfilt(name)` returns the first-level biorthogonal filters for Kingsbury's Q-shift complex dual-tree transform specified by `name`.```

## Examples

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Obtain the decomposition and reconstruction filters associated with the biorthogonal wavelet `nearsym5_7`.

```fname = 'nearsym5_7'; [LoD,HiD,LoR,HiR] = qbiorthfilt(fname);```

Use the `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')```

## Input Arguments

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First-level biorthogonal filter used in Kingsbury's Q-shift complex dual-tree transform, specified by one of the values listed here.

• `'nearsym5_7'` — (5,7)-tap near-orthogonal filter [1]

• `'nearsym13_19'` — (13,19)-tap near-orthogonal filter [2]

• `'antonini'` — (9,7)-tap Antonini filter [1]

• `'legall'` — LeGall 5/3 filter [3]

## Output Arguments

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Lowpass (scaling) analysis filter associated with the biorthogonal filter `name`, returned as a real-valued vector. The length of `LoD` does not equal the length of `HiD`.

Highpass (wavelet) analysis filter associated with the biorthogonal filter `name`, returned as a real-valued vector. The length of `LoD` does not equal the length of `HiD`.

Lowpass (scaling) synthesis filter associated with the biorthogonal filter `name`, returned as a real-valued vector. The length of `LoR` does not equal the length of `HiR`.

Highpass (wavelet) synthesis filter associated with the biorthogonal filter `name`, returned as a real-valued vector. The length of `LoR` does not equal the length of `HiR`.

## References

[1] 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.

[2] 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.

[3] 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.

## Version History

Introduced in R2020a