Discrete stationary wavelet transform 1-D

`SWC = swt(X,N,'`

* wname*')

SWC = swt(X,N,Lo_D,Hi_D)

[SWA,SWD] = swt(___)

`swt`

performs a multilevel
1-D stationary wavelet decomposition using either an orthogonal or
a biorthogonal wavelet. Specify the wavelet using its name (* 'wname'*,
see

`wfilters`

for more information)
or its 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 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`

.

`swt`

is defined using periodic extension. The length of the
approximation and detail coefficients computed at each level equals the length of
the signal.

Given a signal *s* of length *N*,
the first step of the SWT produces, starting from *s*,
two sets of coefficients: approximation coefficients *cA _{1}* and
detail coefficients

`Lo_D`

for approximation, and
with the high-pass filter `Hi_D`

for detail.More precisely, the first step is

*cA _{1}* and

`N`

instead of `N/2`

as
in the DWT case.The next step splits the approximation coefficients *cA _{1}* in
two parts using the same scheme, but with modified filters obtained
by upsampling the filters used for the previous step and replacing

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.