lwtcoef

Extract or reconstruct 1-D LWT wavelet coefficients and orthogonal projections

Since R2021a

Syntax

y = lwtcoef(ca,cd)

y = lwtcoef(ca,cd,Name,Value)

Description

y = lwtcoef(ca,cd) returns the level 1 approximation coefficients that correspond to the approximation and detail coefficients, ca and cd, respectively. ca and cd are outputs of lwt.

y = lwtcoef(ca,cd,Name,Value) specifies options using one or more name-value arguments. For example, y = lwtcoef(ca,cd,'OutputType','coefficients') specifies coefficients output.

Examples

Reconstruct Signal from Orthogonal Projections

Load a 1-D signal of length 2048. Plot the signal.

load wecg
plot(wecg)
title('Signal')
ylabel('Amplitude')
axis tight

Create a lifting scheme associated with the db4 wavelet. Use the lifting scheme to obtain the wavelet decomposition of the signal to the maximum level. Confirm the length of the detail coefficients cell array equals floor(log2(N)), where N is the length of the signal.

wv = 'db4';
lsc = liftingScheme('Wavelet',wv);
[ca,cd] = lwt(wecg,'LiftingScheme',lsc);
[length(cd) floor(log2(length(wecg)))]

ans = 1×2

    11    11

Extract and plot the approximation coefficients at level 3. Confirm the length of the extraction is one-eighth the length of the original signal.

approxCf = lwtcoef(ca,cd,'LiftingScheme',lsc, ...
    'OutputType','coefficients', ...
    'Level',3);
[2048/(2^3) length(approxCf)]

ans = 1×2

   256   256

plot(approxCf)
title('Level 3 Approximation Coefficients')
ylabel('Amplitude')
axis tight

Obtain the orthogonal projection of the level 3 approximation coefficients. Also obtain the orthogonal projections of the detail coefficients at levels 1, 2, and 3. Plot the results.

approx3 = lwtcoef(ca,cd,'LiftingScheme',lsc, ...
    'OutputType','projection','Level',3);
det3 = lwtcoef(ca,cd,'LiftingScheme',lsc, ...
    'OutputType','projection','Level',3,'Type','detail');
det2 = lwtcoef(ca,cd,'LiftingScheme',lsc, ...
    'OutputType','projection','Level',2,'Type','detail');
det1 = lwtcoef(ca,cd,'LiftingScheme',lsc, ...
    'OutputType','projection','Level',1,'Type','detail');
tiledlayout(4,1)
nexttile
plot(approx3)
title('Projection - Approximation')
axis tight
nexttile
plot(det3)
title('Projection - Level 3 Details')
axis tight
nexttile
plot(det2)
title('Projection - Level 2 Details')
axis tight
nexttile
plot(det1)
title('Projection - Level 1 Details')
axis tight

Confirm the sum of the four projections equals the original signal.

max(abs(wecg-(approx3+det3+det2+det1)))

ans = 
1.3323e-15

Input Arguments

ca — Approximation coefficients

scalar | vector | matrix

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

Data Types: single | double
Complex Number Support: Yes

cd — Detail coefficients

cell array

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.

Data Types: single | double
Complex Number Support: Yes

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: y = lwtcoef(ca,cd,'LiftingScheme',lsc,'OutputType','coefficients','Level',2) uses the lifting scheme lsc to extract the approximation coefficients at level 2.

Wavelet — Wavelet

'db1' (default) | character vector | string scalar

Orthogonal or biorthogonal wavelet, 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 match the wavelet you used to generate ca and cd.

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

LiftingScheme — Lifting scheme

liftingScheme object

Lifting scheme to use, specified as a liftingScheme object. For perfect reconstruction, the specified lifting scheme must match the lifting scheme you used to generate ca and cd.

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

OutputType — Output type

'coefficients' (default) | 'projection'

Output type, specified as one of:

• 'coefficients' — Extract the approximation or details coefficients

• 'projection' — Return the projection (reconstruction) of the approximation or details coefficients

Example: y = lwtcoef(ca,cd,'OutputType','projection','Type','detail') returns the projection corresponding to the detail coefficients at the finest scale.

Type — Type of coefficients

'approximation' (default) | 'detail'

Type of coefficients to extract or reconstruct, specified as 'approximation' or 'detail'.

Example: y = lwtcoef(ca,cd,'Type','detail') extracts the detail coefficients at the finest scale.

Level — Level

1 (default) | integer

Level of coefficients to extract or reconstruct, specified as an integer in the range [1,N], where N is the length of cd.

Example: y = lwtcoef(ca,cd,'LiftingScheme',lsc,'Level',3) uses the lifting scheme lsc to extract the approximation coefficients at level 3.

Data Types: double

Int2Int — Handling integer-valued data

false or 0 (default) | true or 1

Handling integer-valued data, specified as one of these:

• 1 (true) — Preserve integer-valued data

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

Int2Int must match the value you used to generate ca and cd.

Example: y = lwtcoef(ca,cd,Int2Int=true) preserves integer-valued data.

Extension — Extension mode

"periodic" (default) | "zeropad" | "symmetric"

Extension mode to use to extract or reconstruct the coefficients, specified as one of these:

• "periodic" — Periodized extension

• "zeropad" — Zero extension

• "symmetric" — Symmetric extension

This argument specifies how to extend the signal at the boundaries. The extension mode must match the value you used to generate ca and cd.

Example: y = lwtcoef(ca,cd,Extension="zeropad") specifies zero extension.

Output Arguments

y — Extracted coefficients or projection

vector | matrix

Extracted coefficients or projection, returned as a vector or matrix. If ca is a scalar or vector, and the elements of cd are vectors, then y is a vector. If ca and the elements of cd are matrices, then y is a matrix, where each column is the extraction or projection of the corresponding columns in ca and cd.

Data Types: single | double

Extended Capabilities

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

Version History

Introduced in R2021a

R2021a: lwtcoef input syntax has changed

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

Functionality	Result	Use Instead	Compatibility Considerations
Y = lwtcoef(TYPE,XDEC,LS,LEVEL,LEVEXT)	Errors	Y = lwtcoef(CA,CD,Name,Value) with the lifting decomposition CA and CD in place of XDEC, and the following name-value arguments: Replace LS with 'LiftingScheme', where 'LiftingScheme' is a liftingScheme object. Replace LEVEXT with 'Level'. Replace TYPE with the Type and OutputType name-value arguments. LEVEL is no longer needed.	According to the value of TYPE, set the Type and OutputType name-value arguments as listed: 'a' — 'Type','approximation' and 'OutputType','projection' 'ca' — 'Type','approximation' and 'OutputType','coefficients' 'd' — 'Type','detail' and 'OutputType','projection' 'cd' — 'Type','detail' and 'OutputType','coefficients'