2.2. Smoothing¶
2.2.1. Spectral Filters¶
2.2.2. Savitzky-Golay filter¶
Smoothing filter using Savitzky-Golay filter
import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
x,fs = sp.data.ppg_sample(sample=1)
x = x[:int(fs*5)]
x = x - x.mean()
t = np.arange(len(x))/fs
xf1 = sp.filter_smooth_sGolay(x.copy(),window_length=31, polyorder=2)
xf2 = sp.filter_smooth_sGolay(x.copy(),window_length=31, polyorder=5)
xf3 = sp.filter_smooth_sGolay(x.copy(),window_length=51, polyorder=3)
2.2.3. Gaussian Filter¶
Smoothing filter using Gaussian Kernel and 1d-ConvFB
Smoothing filter using Gaussian Kernel and 1d-ConvFB
sigma : sigma for gaussian kernel, if None, sigma=window_length/6
import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
x,fs = sp.data.ppg_sample(sample=1)
x = x[:int(fs*5)]
x = x - x.mean()
t = np.arange(len(x))/fs
xf1 = sp.filter_smooth_gauss(x.copy(),window_length=31, sigma_scale=2.7)
xf2 = sp.filter_smooth_gauss(x.copy(),window_length=31, sigma_scale=5.4)
xf3 = sp.filter_smooth_gauss(x.copy(),window_length=51, sigma_scale=2.7)
2.2.4. Mollifier¶
Smoothing filter using Mollifier kernel and 1d-ConvFB
Smoothing filter using Mollifier kernel and 1d-ConvFB
Mollifier: Kurt Otto Friedrichs
Generalized function
\[f(x) = exp(-s/(1-|x|**p)) for |x|<1, x \in [-r, r]\]Convolving with a mollifier, signals’s sharp features are smoothed, while still remaining close to the original nonsmooth (generalized) signals.
Intuitively, given a function which is rather irregular, by convolving it with a mollifier the function gets “mollified”.
This function is infinitely differentiable, non analytic with vanishing derivative for |x| = 1, can be therefore used as mollifier as described in [1]. This is a positive and symmetric mollifier.[2]
2.2.5. Wavelet Filtering¶
Wavelet Filtering is covered in seperate section in more detail
wavelet_filtering
References
Click for more details
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