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Stationary Wavelet Transform

Stationary Wavelet Transform (SWT), 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

pywt.swt(data, wavelet, level=None, start_level=0)

Performs multilevel Stationary Wavelet Transform.

Parameters:

data :

Input signal

wavelet :

Wavelet to use (Wavelet object or name)

level : int, optional

Transform level.

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)

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 m = start_level is given, then the beginning m steps are skipped:

[(cAm+n, cDm+n), ..., (cAm+1, cDm+1), (cAm, cDm)]

Multilevel swt2

pywt.swt2(data, wavelet, level, start_level=0)

2D Stationary Wavelet Transform.

Parameters:

data : ndarray

2D array with input data

wavelet : Wavelet object or name string

Wavelet to use

level : int

How many decomposition steps to perform

start_level : int, optional

The level at which the decomposition will start (default: 0)

Returns:

coeffs : list

Approximation and details coefficients:

[
    (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 and n is start_level.

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.