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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) 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) 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. max_level : int Maximum level of Stationary Wavelet Transform for data of given length.