ilwt

Inverse 1-D lifting wavelet transform

Description

xr = ilwt(ca,cd) returns the 1-D inverse wavelet transform based on the approximation coefficients, ca, and cell array of detail coefficients, cd. By default, ilwt assumes you used the lifting scheme associated with the db1 wavelet to obtain ca and cd. If you do not modify the coefficients, xr is a perfect reconstruction of the signal.

example

xr = ilwt(ca,cd,Name,Value) specifies options using one or more name-value arguments. For example, xr = ilwt(ca,cd,'Wavelet','db2') specifies the orthogonal wavelet db2.

For perfect reconstruction, all name-value arguments must match those used in lwt to obtain ca and cd.

Examples

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Create a lifting scheme associated with the db3 wavelet. Specify an integer-valued signal whose length is a power of 2.

lsc = liftingScheme('Wavelet','db3');
n = 8;
sig = 1:2^n;

Use the lifting scheme to obtain the integer-valued LWT of the signal down to the maximum decomposition level.

[ca,cd] = lwt(sig,'LiftingScheme',lsc,'Int2Int',true);

Confirm the detail coefficients cd are a cell array whose length is equal to the exponent of 2.

length(cd)
ans = 8

Obtain the inverse LWT up to level 0. Confirm perfect reconstruction.

xrec0 = ilwt(ca,cd,'LiftingScheme',lsc,'Int2Int',true,'Level',0);
max(abs(xrec0(:)-sig(:)))
ans = 0

Obtain the inverse LWT up to level 1.

xrec1 = ilwt(ca,cd,'LiftingScheme',lsc,'Int2Int',true,'Level',1);

Obtain the level 1 decomposition of the signal. Confirm the approximation coefficients are equal to xrec1.

[ca,cd] = lwt(sig,'LiftingScheme',lsc,'Int2Int',true,'Level',1);
max(abs(ca(:)-xrec1(:)))
ans = 0

Load the 23 channel EEG data Espiga3. The channels are arranged column-wise.

size(Espiga3)
ans = 1×2

995    23

Obtain the LWT of the multichannel signal using the db4 wavelet down to the default maximum decomposition level.

wv = 'db4';
[ca,cd] = lwt(Espiga3,'Wavelet',wv);

Reconstruct the multichannel signal.

xrec = ilwt(ca,cd,'Wavelet',wv);

Because the original signal has an odd number of samples in each channel, confirm the reconstruction has one more row than the original signal.

size(xrec)
ans = 1×2

996    23

Confirm the last row in the reconstruction is equal to the previous row.

max(abs(xrec(end-1,:)-xrec(end,:)))
ans = 5.6843e-14

Delete the last row from the reconstruction. Confirm the result is equal to the original signal.

xrec(end,:) = [];
max(abs(Espiga3(:)-xrec(:)))
ans = 4.5475e-13

Input Arguments

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Approximation (lowpass) coefficients at the coarsest level, specified as a scalar, vector, or matrix. The coefficients are the output of lwt.

If ca and the elements of cd are matrices, xr is a matrix where each column is the inverse wavelet transform of the corresponding columns in ca and cd.

Data Types: single | double
Complex Number Support: Yes

Detail coefficients, specified as an L-by-1 cell array, where L is the level of the transform. The elements of cd are in order of decreasing resolution. The coefficients are the output of lwt.

If ca and the elements of cd are matrices, xr is a matrix where each column is the inverse wavelet transform of the corresponding columns in ca and cd.

Data Types: single | double
Complex Number Support: Yes

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: xr = ilwt(ca,cd,'LiftingScheme',lsc,'Level',1) uses the lsc lifting scheme to perform an inverse wavelet transform up to level 1.

Orthogonal or biorthogonal wavelet to use in the inverse LWT, specified as a character vector or string scalar. See the Wavelet property of liftingScheme for the list of supported wavelets. For perfect reconstruction, the specified wavelet must be the same wavelet that was used to obtain the coefficients ca and cd.

You cannot specify 'Wavelet' and 'LiftingScheme' name-value arguments at the same time.

Example: xr = ilwt(ca,cd,'Wavelet','bior3.5') uses the bior3.5 biorthogonal wavelet.

Data Types: char | string

Lifting scheme to use in the inverse LWT, specified as a liftingScheme object. For perfect reconstruction, the specified lifting scheme must be the same lifting scheme that was used to obtain the coefficients ca and cd.

You cannot specify 'Wavelet' and 'LiftingScheme' name-value arguments at the same time.

Example: xr = ilwt(ca,cd,'LiftingScheme',lScheme) uses the lScheme lifting scheme.

Reconstruction level, specified as a nonnegative integer less than or equal to length(cd)-1. If unspecified, the reconstruction level defaults to 0 and xr is a perfect reconstruction of the signal.

Example: xr = ilwt(ca,cd,'Level',1) reconstructs the signal up to level 1.

Data Types: double

Extension mode to use in the inverse LWT, specified as a 'periodic' (default), 'zeropad', or 'symmetric'. The value of 'Extension' specifies how to extend the signal at the boundaries.

Example: xr = ilwt(ca,cd,'Extension','symmetric') specifies the symmetric extension mode.

Integer-valued data handling, specified as a numeric or logical 1 (true) or 0 (false).

• 1 (true) — Preserve integer-valued data

• 0 (false) — Do not preserve integer-valued data

Specify the 'Int2Int' name-value argument only if all elements of the input are integers.

Example: xr = ilwt(ca,cd,'Int2Int',true) preserves integer-valued data.

Output Arguments

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Inverse wavelet transform of ca and cd, returned as a vector or matrix. If ca is a scalar or vector, and the elements of cd are vectors, xr is a vector. If ca and the elements of cd are matrices, xr is a matrix where each column is the inverse wavelet transform of the corresponding columns in ca and cd.

Data Types: single | double

Compatibility Considerations

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Behavior changed in R2021a

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™. 