spkit.wavelet_filtering

spkit.wavelet_filtering(x, wv='db3', threshold='optimal', filter_out_below=True, k=1.5, mode='elim', show=False, wpd_mode='symmetric', wpd_maxlevel=None, packetwise=False, WPD=False, lvl=[], verbose=False, fs=128.0, sf=1, IPR=[0.25, 0.75], figsize=(11, 6), plot_abs_coef=False)

Wavelet Filtering

Wavelet Filtering

Wavelet filtering is applied on signal by decomposing signal into wavelet domain, filtering out wavelet coefficients and reconstructing signal back. Signal is decompose using DWT with wavelet function specified as wv (e.g. db3), and filtering out coefficients using by threshold, mode, and filter_out_below arguments.

1. Wavelet Transform

   \(W(k) = DWT(x(n))\)

2. Filtering (with elim mode) - \(W(k)=0\)

   • if \(|W(k)|<=threshold\) and if filter_out_below = True

   • if \(|W(k)|>threshold\) and if filter_out_below = False

3. Reconstruction

   \(x'(n) = IDWT(W(k))\)

Parameters:

x: 1d array

Threshold Computation method:

threshold: ‘str’ or float, default - ‘optimal’

• if str, method to compute threshold, example : ‘optimal’, ‘sd’, ‘iqr’

• ‘optimal’: threshold = sig*sqrt(2logN), sig = median(|w|)/0.6745

• ‘sd’ : threshold = k*SD(w)

• ‘iqr’: threshold = q3+kr, threshold_l =q1-kr, where r = IQR(w) #Tukey’s fences

• ‘ttt’: Modified Thompson Tau test (ttt) # TODO

wvstr, ‘db3’(default)

• Wavelet family

• {‘db3’…..’db38’, ‘sym2…..sym20’, ‘coif1…..coif17’, ‘bior1.1….bior6.8’, ‘rbio1.1…rbio6.8’, ‘dmey’}

mode: str, default = ‘elim’

• ‘elim’ - remove the coeeficient (by zering out),

• ‘clip’ - cliping the coefficient to threshold

filter_out_below: bool, default True,

• if true, wavelet coefficient below threshold are eliminated else obove threshold

wpd_mode = str, default ‘symmetric’

• Wavelet Decomposition modes

• [‘zero’, ‘constant’, ‘symmetric’, ‘periodic’, ‘smooth’, ‘periodization’]

wpd_maxlevel: int

• level of decomposition,

  if None, max level posible is used

packetwise: bool, if true,

• thresholding is applied to each packet/level individually, else globally

WPD: if true,

• WPD is applied as wavelet transform

lvl: list

list of levels/packets apply the thresholding, if empty, applied to all the levels/packets

show: bool, deafult=False,

• if to plot figure, it True, following are used

figsize: default=(11,6), size of figure plot_abs_coef: bool, deafult=False,

if True,plot abs coefficient value, else signed

Returns:

xR: filtered signal, same size as x

See also

wavelet_filtering_win

applying wavelet filtering on smaller windows

filter_X

spectral filtering

Notes

#TODO

References

• wikipedia -

Examples

import spkit as sp
x,fs = sp.load_data.eeg_sample_1ch()
xr = sp.wavelet_filtering(x,fs=fs, wv='db3', threshold='optimal',show=True)

#################

import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
x = sp.create_signal_1d(n=1000,seed=1,sg_polyorder=5, sg_winlen=11)
x = sp.add_noise(x,snr_db=10)
xr = sp.wavelet_filtering(x.copy(),wv='db3',threshold='optimal',show=True)

Examples using spkit.wavelet_filtering

Wavelet Filtering

Wavelet Filtering