liftfilt

R2026b

Apply elementary lifting steps on filters

Syntax

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

[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,LoR,NormalizationFactor=NF)

liftfilt(___)

Description

[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

Generate Biorthogonal Wavelet Filters From Haar Filters

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

LoD,LoR — Lowpass filters

real-valued vectors

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

ELS — Lifting steps

structure array

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

NF — Normalization factor

nonzero scalar

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

LoDN,HiDN — Decomposition filters

real-valued vectors

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

Data Types: double

LoRN,HiRN — Reconstruction filters

real-valued vectors

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

Data Types: double

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Plotting is not supported.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Refer to the usage notes and limitations in the C/C++ Code Generation section. The same usage notes and limitations apply to GPU code generation.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The liftfilt function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2021b

R2026b: Use thread-based environments

You can use liftfilt in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

R2021b: liftfilt input syntax has changed

The liftfilt input syntax has changed. Use name-value arguments instead.

Functionality	Result	Use Instead	Compatibility Considerations
[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,HiD,LoR,HiR,ELS)	Errors	[LoDN,HiDN,LoRN,HiRN] = liftfilt(LoD,LoR,LiftingSteps=ELS), where ELS is a structure array consisting of elementary lifting steps.	You can also scale the filters by a normalization factor. For more information about elementary lifting steps, see liftingStep.
liftfilt(LoD,HiD,LoR,HiR,ELS,TYPE,VALUE)	Errors	NA	This syntax is no longer supported.