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.. currentmodule:: pywt
.. include:: ../substitutions.rst
Stationary Wavelet Transform
----------------------------
`Stationary Wavelet Transform (SWT) <http://en.wikipedia.org/wiki/Stationary_wavelet_transform>`_,
also known as *Undecimated wavelet transform* or *Algorithme à trous* is a translation-invariance
modification of the *Discrete Wavelet Transform* that does not decimate coefficients at every
transformation level.
Multilevel ``swt``
~~~~~~~~~~~~~~~~~~
.. function:: swt(data, wavelet, level[, start_level=0])
Performs multilevel Stationary Wavelet Transform.
:param data: |data|
:param wavelet: |wavelet|
:param int level: Required transform level. See the :func:`swt_max_level` function.
:param int start_level: The level at which the decomposition will begin (it
allows to skip a given number of transform steps and compute coefficients
starting directly from the *start_level*)
.. compound::
Returns list of coefficient pairs in the form::
[(cAn, cDn), ..., (cA2, cD2), (cA1, cD1)]
where *n* is the *level* value.
If *m* = *start_level* is given, then the beginning *m* steps are
skipped::
[(cAm+n, cDm+n), ..., (cAm+1, cDm+1), (cAm, cDm)]
Multilevel ``swt2``
~~~~~~~~~~~~~~~~~~~~~
.. function:: swt2(data, wavelet, level[, start_level=0])
Performs multilevel 2D Stationary Wavelet Transform.
:param data: 2D array with input data.
:param wavelet: |wavelet|
:param level: Number of decomposition steps to perform.
:param start_level: The level at which the decomposition will begin.
.. compound::
The result is a set of coefficients arrays over the range of decomposition
levels::
[
(cA_n,
(cH_n, cV_n, cD_n)
),
(cA_n+1,
(cH_n+1, cV_n+1, cD_n+1)
),
...,
(cA_n+level,
(cH_n+level, cV_n+level, cD_n+level)
)
]
where *cA* is approximation, *cH* is horizontal details, *cV* is vertical
details, *cD* is diagonal details, *n* is *start_level* and *m* equals
*n+level*.
Maximum decomposition level - ``swt_max_level``
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.. function:: swt_max_level(input_len)
Calculates the maximum level of Stationary Wavelet Transform for data of
given length.
:param input_len: Input data length.
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