iswt :: Functions (Wavelet Toolbox™)

iswt

Purpose

Inverse discrete stationary wavelet transform 1-D

Syntax

X = iswt(SWC,'wname')
X = iswt(SWA,SWD,'wname')
X = iswt(SWC,Lo_R,Hi_R)
X = iswt(SWA,SWD,Lo_R,Hi_R)

Description

iswt performs a multilevel 1-D stationary wavelet reconstruction using either a specific orthogonal wavelet ('wname', see wfilters for more information) or specific reconstruction filters (Lo_R and Hi_R).

X = iswt(SWC,'wname') or X = iswt(SWA,SWD,'wname') or X = iswt(SWA(end,:),SWD,'wname') reconstructs the signal X based on the multilevel stationary wavelet decomposition structure SWC or [SWA,SWD] (see swt for more information).

X = iswt(SWC,Lo_R,Hi_R) or X = iswt(SWA,SWD,Lo_R,Hi_R) or X = iswt(SWA(end,:),SWD,Lo_R,Hi_R) reconstruct as above, using filters that you specify.

Lo_R is the reconstruction low-pass filter.
Hi_R is the reconstruction high-pass filter.

Lo_R and Hi_R must be the same length.

Examples

% Load original 1D signal.
load noisbloc; s = noisbloc;
                
% Perform SWT decomposition at level 3 of s using db1.
swc = swt(s,3,'db1');
% Second usage.
[swa,swd] = swt(s,3,'db1');

% Reconstruct s from the stationary wavelet
% decomposition structure swc.
a0 = iswt(swc,'db1');
% Second usage.
a0bis = iswt(swa,swd,'db1');


% Check for perfect reconstruction.
err = norm(s-a0)
err =
  9.6566e-014

errbis = norm(s-a0bis)
errbis =
  9.6566e-014

Algorithm

See the section "Stationary Wavelet Transform" in Chapter 6, "Advanced Concepts", of the User's Guide.

References

Nason, G.P.; B.W. Silverman (1995), "The stationary wavelet transform and some statistical applications," Lecture Notes in Statistics, 103, pp. 281-299.

Coifman, R.R.; Donoho D.L. (1995), "Translation invariant de-noising," Lecture Notes in Statistics, 103, pp 125-150.

Pesquet, J.C.; H. Krim, H. Carfatan (1996), "Time-invariant orthonormal wavelet representations," IEEE Trans. Sign. Proc., vol. 44, 8, pp. 1964-1970.

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