# iswt

Inverse discrete stationary wavelet transform 1-D

## Description

x = iswt(swc,wname) reconstructs the 1-D signal x based on the multilevel stationary wavelet decomposition swc using the wavelet specified by wname. swc is expected to be the output of the swt function. The wname wavelet must be the same wavelet used to obtain the swc structure.

x = iswt(swa,swd,wname) uses the approximation coefficients swa and detail coefficients swd to reconstruct the 1-D signal. The real-valued matrices swa and swd are expected to be the outputs of the swt function.

The syntax iswt(swa(end,:),swd,wname) is equivalent to iswt(swa,swd,wname).

x = iswt(swc,LoR,HiR) uses the scaling filter LoR and wavelet filter HiR. The filters are expected to be the reconstruction filters associated with the wavelet used to create the swc structure. For more information, see wfilters.

x = iswt(swa,swd,LoR,HiR) uses the scaling filter LoR and wavelet filter HiR. The filters are expected to be the reconstruction filters associated with the wavelet used to create the swc structure. For more information, see wfilters.

The syntax iswt(swa(end,:),swd,LoR,HiR) is equivalent to iswt(swa,swd,LoR,HiR).

example

## Examples

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Demonstrate perfect reconstruction using swt and iswt with a biorthogonal wavelet.

[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters('bior3.5');
[swa,swd] = swt(noisbloc,3,Lo_D,Hi_D);
recon = iswt(swa,swd,Lo_R,Hi_R);
norm(noisbloc-recon)
ans =
1.0933e-13

## Input Arguments

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Multilevel stationary wavelet decomposition, specified as a real-valued matrix. swc is the output of swt.

Data Types: double

Wavelet, specified as a character vector or string scalar. iswt supports only Type 1 (orthogonal) or Type 2 (biorthogonal) wavelets. See wfilters for a list of orthogonal and biorthogonal wavelets.

Approximation coefficients, specified as a real-valued matrix. swa is the output of swt.

Data Types: double

Detail coefficients, specified as a real-valued matrix. swd is the output of swt.

Data Types: double

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

Data Types: double

## References

[1] Nason, G. P., and B. W. Silverman. “The Stationary Wavelet Transform and Some Statistical Applications.” In Wavelets and Statistics, edited by Anestis Antoniadis and Georges Oppenheim, 103:281–99. New York, NY: Springer New York, 1995. https://doi.org/10.1007/978-1-4612-2544-7_17.

[2] Coifman, R. R., and D. L. Donoho. “Translation-Invariant De-Noising.” In Wavelets and Statistics, edited by Anestis Antoniadis and Georges Oppenheim, 103:125–50. New York, NY: Springer New York, 1995. https://doi.org/10.1007/978-1-4612-2544-7_9.

[3] Pesquet, J.-C., H. Krim, and H. Carfantan. “Time-Invariant Orthonormal Wavelet Representations.” IEEE Transactions on Signal Processing 44, no. 8 (August 1996): 1964–70. https://doi.org/10.1109/78.533717.

## Version History

Introduced before R2006a