Stationary Wavelet Transform¶
Stationary Wavelet Transform (SWT), also known as Undecimated wavelet transform or Algorithme à trous is a translationinvariance modification of the Discrete Wavelet Transform that does not decimate coefficients at every transformation level.
Multilevel 1D swt
¶

pywt.
swt
(data, wavelet, level=None, start_level=0, axis=1)¶ Multilevel 1D stationary wavelet transform.
Parameters: data :
Input signal
wavelet :
Wavelet to use (Wavelet object or name)
level : int, optional
The number of decomposition steps to perform.
start_level : int, optional
The level at which the decomposition will begin (it allows one to skip a given number of transform steps and compute coefficients starting from start_level) (default: 0)
axis: int, optional
Axis over which to compute the SWT. If not given, the last axis is used.
Returns: coeffs : list
List of approximation and details coefficients pairs in order similar to wavedec function:
[(cAn, cDn), ..., (cA2, cD2), (cA1, cD1)]
where n equals input parameter
level
.If
start_level = m
is given, then the beginning m steps are skipped:[(cAm+n, cDm+n), ..., (cAm+1, cDm+1), (cAm, cDm)]
Notes
The implementation here follows the “algorithm atrous” and requires that the signal length along the transformed axis be a multiple of
2**level
. If this is not the case, the user should pad up to an appropriate size using a function such asnumpy.pad
.
Multilevel 2D swt2
¶

pywt.
swt2
(data, wavelet, level, start_level=0, axes=(2, 1))¶ Multilevel 2D stationary wavelet transform.
Parameters: data : array_like
2D array with input data
wavelet : Wavelet object or name string, or 2tuple of wavelets
Wavelet to use. This can also be a tuple of wavelets to apply per axis in
axes
.level : int
The number of decomposition steps to perform.
start_level : int, optional
The level at which the decomposition will start (default: 0)
axes : 2tuple of ints, optional
Axes over which to compute the SWT. Repeated elements are not allowed.
Returns: coeffs : list
Approximation and details coefficients:
[ (cA_m, (cH_m, cV_m, cD_m) ), (cA_m+1, (cH_m+1, cV_m+1, cD_m+1) ), ..., (cA_m+level, (cH_m+level, cV_m+level, cD_m+level) ) ]
where cA is approximation, cH is horizontal details, cV is vertical details, cD is diagonal details and m is
start_level
.Notes
The implementation here follows the “algorithm atrous” and requires that the signal length along the transformed axes be a multiple of
2**level
. If this is not the case, the user should pad up to an appropriate size using a function such asnumpy.pad
.
Multilevel ndimensional swtn
¶

pywt.
swtn
(data, wavelet, level, start_level=0, axes=None)¶ ndimensional stationary wavelet transform.
Parameters: data : array_like
ndimensional array with input data.
wavelet : Wavelet object or name string, or tuple of wavelets
Wavelet to use. This can also be a tuple of wavelets to apply per axis in
axes
.level : int
The number of decomposition steps to perform.
start_level : int, optional
The level at which the decomposition will start (default: 0)
axes : sequence of ints, optional
Axes over which to compute the SWT. A value of
None
(the default) selects all axes. Axes may not be repeated.Returns: [{coeffs_level_n}, …, {coeffs_level_1}]: list of dict
Results for each level are arranged in a dictionary, where the key specifies the transform type on each dimension and value is a ndimensional coefficients array.
For example, for a 2D case the result at a given level will look something like this:
{'aa': <coeffs> # A(LL)  approx. on 1st dim, approx. on 2nd dim 'ad': <coeffs> # V(LH)  approx. on 1st dim, det. on 2nd dim 'da': <coeffs> # H(HL)  det. on 1st dim, approx. on 2nd dim 'dd': <coeffs> # D(HH)  det. on 1st dim, det. on 2nd dim }
For userspecified
axes
, the order of the characters in the dictionary keys map to the specifiedaxes
.Notes
The implementation here follows the “algorithm atrous” and requires that the signal length along the transformed axes be a multiple of
2**level
. If this is not the case, the user should pad up to an appropriate size using a function such asnumpy.pad
.
Maximum decomposition level  swt_max_level
¶

pywt.
swt_max_level
(input_len)¶ Calculates the maximum level of Stationary Wavelet Transform for data of given length.
Parameters: input_len : int
Input data length.
Returns: max_level : int
Maximum level of Stationary Wavelet Transform for data of given length.
Notes
For the current implementation of the stationary wavelet transform, this corresponds to the number of times
input_len
is evenly divisible by two. In other words, for an nlevel transform, the signal length must be a multiple of2**n
.numpy.pad
can be used to pad a signal up to an appropriate length as needed.