# liftfilt

Apply elementary lifting steps on filters

Since R2021b

## Description

example

[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,LoR,LiftingSteps=ELS) returns the four filters obtained by adding an array of elementary lifting steps (ELS) starting from the two filters LoD and LoR.

[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,LoR,NormalizationFactor=NF) scales the filters by the normalization factor NF.

liftfilt(___) with no output arguments plots the successive biorthogonal pairs. A scaling function and a wavelet comprise each pair.

## Examples

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This example shows how to obtain the bior1.3 wavelet filters using Haar filters and elementary lifting steps.

Obtain the Haar lowpass decomposition and reconstruction filters.

[LoD,~,LoR,~] = wfilters("haar");

Use liftingStep to create two elementary lifting steps of type update. Create an array consisting of the two steps.

els1 = liftingStep(Type="update",...
Coefficients=[0.125 -0.125],MaxOrder=0);
els2 = liftingStep(Type="update",...
Coefficients=[0.125 -0.125],MaxOrder=1);
elsBoth = [els1;els2];

Apply the lifting steps to the Haar filters to obtain new filters.

[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,LoR,LiftingSteps=elsBoth);

Obtain the bior1.3 wavelet filters. Confirm that up to a sign change, the wavelet filters are equal to the filters liftfilt returns.

[LoDw,HiDw,LoRw,HiRw] = wfilters("bior1.3");
samewavelet = ...
isequal([LoDw,HiDw,LoRw,HiRw],[LoDN,-HiDN,LoRN,HiRN])
samewavelet = logical
1

Use liftfilt to plot the successive biorthogonal pairs of scaling functions and wavelets.

liftfilt(LoD,LoR,LiftingSteps=elsBoth)

## Input Arguments

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Lowpass filters associated with a wavelet, specified as real-valued vectors. LoD is the lowpass decomposition filter. LoR is the lowpass reconstruction filters.

Example: For [LoD,~,LoR,~] = wfilters("db4"), liftfilt(LoD,LoR,LiftingSteps=lsteps) applies the elementary lifting steps specified in lsteps to the db4 filters.

Data Types: double

Lifting steps, specified as a structure array consisting of elementary lifting steps.

• If liftingStep.Type="update", LoR and HiD are unchanged, where HiD is the associated highpass decomposition filter.

• If liftingStep.Type="predict", LoD and HiR are unchanged, where HiR is the associated highpass decomposition filter.

Example: liftfilt(LoD,LoR,LiftingSteps=ELS) applies the elementary lifting steps specified in lsteps to the filters LoD and LoR.

Data Types: struct

Normalization factor, specified as a nonzero scalar.

Example: [LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,LoR,NF=2) scales the filters by 2.

Data Types: double

## Output Arguments

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Decomposition filters, returned as a pair of real-valued vectors. LoDN and HiDN correspond to the lowpass and highpass filters, respectively.

Data Types: double

Reconstruction filters, returned as a pair of real-valued vectors. LoRN and HiRN correspond to the lowpass and highpass filters, respectively.

Data Types: double

## Version History

Introduced in R2021b

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