Discrete stationary wavelet transform 1D
SWC = swt(X,N,'
wname
')
SWC = swt(X,N,Lo_D,Hi_D)
swt
performs a multilevel
1D 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,'
computes
the stationary wavelet decomposition of the signal wname
')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 lowpass
filter.
Hi_D
is the decomposition highpass
filter.
Lo_D
and Hi_D
must be
the same length.
The output matrix SWC
contains the vectors
of coefficients stored rowwise:
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 rowwise:
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

% 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 denoising," Lecture Notes in Statistics, 103, pp. 125–150.
Pesquet, J.C.; H. Krim, H. Carfatan (1996), "Timeinvariant orthonormal wavelet representations," IEEE Trans. Sign. Proc., vol. 44, 8, pp. 1964–1970.