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swt

Discrete stationary wavelet transform 1-D

Syntax

Description

swt performs a multilevel 1-D stationary wavelet decomposition using either a specific orthogonal wavelet ('wname' see wfilters for more information) or specific orthogonal wavelet decomposition filters.

SWC = swt(X,N,'wname') computes the stationary wavelet decomposition of the signal X at level N, using 'wname'.

N must be a strictly positive integer (see wmaxlev for more information) and length(X) must be a multiple of 2N .

SWC = swt(X,N,Lo_D,Hi_D), computes the stationary wavelet decomposition as above, given these filters as input:

Lo_D and Hi_D must be the same length.

The output matrix SWC contains the vectors of coefficients stored row-wise:

For 1 i N, the output matrix SWC(i,:) contains the detail coefficients of level i and SWC(N+1,:) contains the approximation coefficients of level N.

[SWA,SWD] = swt(...) computes approximations, SWA, and details, SWD, stationary wavelet coefficients.

The vectors of coefficients are stored row-wise:

For 1 i N, the output matrix SWA(i,:) contains the approximation coefficients of level i and the output matrix SWD(i,:) contains the detail coefficients of level i.

Examples

Algorithm

Given a signal s of length N, the first step of the SWT produces, starting from s, two sets of coefficients: approximation coefficients cA1 and detail coefficients cD1. These vectors are obtained by convolving s with the low-pass filter Lo_D for approximation, and with the high-pass filter Hi_D for detail.

More precisely, the first step is

The next step splits the approximation coefficients cA1 in two parts using the same scheme. But, with modified filters obtained by upsampling the filters used for the previous step and replacing s by cA1. Then, the SWT produces cA2 and cD2. More generally,

See Also
dwt, wavedec

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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