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Discrete stationary wavelet transform 1-D
SWC = swt(X,N,'wname')
SWC = swt(X,N,Lo_D,Hi_D)
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 2^{N} .
SWC = swt(X,N,Lo_D,Hi_D) computes the stationary wavelet decomposition as above, given these filters as input:
Lo_D is the decomposition low-pass filter.
Hi_D is the decomposition high-pass filter.
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.
Note swt is defined using dwt with periodic extension. |
% Load original 1D signal. load noisbloc; s = noisbloc; % Perform SWT decomposition at level 3 of s using db1. [swa,swd] = swt(s,3,'db1'); % Plots of SWT coefficients of approximations and details % at levels 3 to 1. % Using some plotting commands, % the following figure is generated.
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.