wrcoef

Reconstruct single branch from 1-D wavelet coefficients

Syntax

x = wrcoef(type,c,l,wname)

x = wrcoef(type,c,l,LoR,HiR)

x = wrcoef(___,n)

Description

x = wrcoef(type,c,l,wname) reconstructs the coefficients vector of type type based on the wavelet decomposition structure [c,l] of a 1-D signal (see wavedec for more information) using the wavelet specified by wname. The coefficients at the maximum decomposition level are reconstructed. The length of x is equal to the length of the original 1-D signal.

x = wrcoef(type,c,l,LoR,HiR) uses the reconstruction filters LoR and HiR.

x = wrcoef(___,n) reconstructs the coefficients at level n using any of the previous syntaxes.

Examples

Reconstruct Wavelet Coefficients

Load a 1-D signal.

load sumsin
s = sumsin;

Perform a level 5 wavelet decomposition of the signal using the sym4 wavelet.

[c,l] = wavedec(s,5,'sym4');

Reconstruct the approximation coefficients at level 5 from the wavelet decomposition structure [c,l].

a5 = wrcoef('a',c,l,'sym4');

Reconstruct the detail coefficients at level 2.

d2 = wrcoef('d',c,l,'sym4',2);

Plot the original signal and reconstructed coefficients.

subplot(3,1,1)
plot(s)
title('Original Signal')
subplot(3,1,2)
plot(a5)
title('Reconstructed Approximation At Level 5')
subplot(3,1,3)
plot(d2)
title('Reconstructed Details At Level 2')

Multiresolution Analysis Based on Decimated Discrete Wavelet Transform

This example shows how, starting with a multilevel 1-D discrete wavelet decomposition of a signal, you can obtain projections of the signal onto wavelet subspaces at successive scales and a scaling subspace. These projections are at the same time scale as the original signal. In other words, you can obtain a multiresolution analysis (MRA) based on the decimated discrete wavelet transform (DWT). You can recover the signal by summing the projections. For more information, see Practical Introduction to Multiresolution Analysis.

Load and plot a signal.

load noissin
plot(noissin)
title("Original Signal")

Use the wavedec function to obtain the discrete wavelet decomposition of the signal down to level 3 using the db4 wavelet.

level = 3;
wv = "db4";
[C,L] = wavedec(noissin,level,wv);

Preallocate a matrix to save the MRA. The number of rows is one more than the level of decomposition, and the number of columns equals the length of the signal.

mra = zeros(level+1,numel(noissin));

Use the wrcoef function to obtain the projections of the signal onto the three wavelet (detail) subspaces. Then obtain the projection onto the final scaling (coarse or approximation) subspace.

for k=1:level
    mra(k,:) = wrcoef("d",C,L,wv,k);
end
mra(end,:) = wrcoef("a",C,L,wv,level);

Confirm the sum along the rows of the MRA equals the original signal.

mraSum = sum(mra,1);
max(abs(mraSum-noissin))

ans = 
1.6591e-12

Plot the MRA.

tiledlayout(level+1,1)
for k=1:level
    nexttile
    plot(mra(k,:))
    title("Projection Onto Detail Subspace "+num2str(k))
end
nexttile
plot(mra(end,:))
title("Projection Onto Approximation Subspace")

Input Arguments

type — Coefficients to reconstruct

'a' | 'd'

Coefficients to reconstruct, specified as 'a' or 'd', for approximation or detail coefficients, respectively.

c — Wavelet decomposition

real-valued vector

Wavelet decomposition of a 1-D signal, specified as a real-valued vector. The vector contains the wavelet coefficients. The bookkeeping vector l contains the coefficients by level. See wavedec.

Data Types: double | single

l — Bookkeeping vector

vector of positive integers

Bookkeeping vector, specified as a vector of positive integers. The bookkeeping vector is used to parse the coefficients in the wavelet decomposition c by level. See wavedec.

Data Types: double | single

wname — Analyzing wavelet

character vector | string scalar

Analyzing wavelet used to create the wavelet decomposition structure [c,l], specified as a character vector or string scalar. wrcoef supports only orthogonal or biorthogonal wavelets. See wfilters.

LoR,HiR — Wavelet reconstruction filters

even-length real-valued vectors

Wavelet reconstruction filters, specified as a pair of even-length real-valued vectors. LoR is the lowpass reconstruction filter, and HiR is the highpass reconstruction filter. The lengths of LoR and HiR must be equal. See wfilters for additional information.

n — Coefficients level

length(l)-2 | nonnegative integer

Coefficients level, specified as a nonnegative integer. When type is 'a', n is allowed to be 0. Otherwise, n is a strictly positive integer such that n ≤ length(l)-2. The default value of n is length(l)-2.

Version History

Introduced before R2006a