Doc mention cutoff frequency correction for signal.filtfilt

The filtfilt function runs two filters to cancel the phase shift. Hence to compensate for the twice -3dB attenuation, one should define a higher cutoff frequency equal to f_c = f_wanted / 0.8 . See explanations in https://nbviewer.jupyter.org/github/demotu/BMC/blob/master/notebooks/DataFiltering.ipynb, Cell[8] This should be mentioned in the doc and the examples changed appropriately for filtfilt and lfilter

Simple example:

import numpy as np
import scipy
import scipy.signal
import matplotlib.pyplot as plt

f0 = 0.1
N = 2
rip = 0.05

x = np.linspace(0,100, 1001)
y = np.random.randn(len(x))

cutoffs = [None, f0, f0, f0/0.8, f0*0.8]
lss = ["-", "--", ":", ":", ":"]
labels = ["raw", "single pass", "dp: no corr", "dp: good corr", "dp: bad corr"]
Y = np.vstack((y, ys, yf, yff, yfff))

fig,ax = plt.subplots(figsize=(16,12))
single_pass=True
for cutoff, label, ls in zip(cutoffs, labels, lss):
    if cutoff is None:
        yf = y
    else:
        b, a = scipy.signal.cheby1(N, rip, cutoff)
        if single_pass:
            yf = scipy.signal.lfilter(b, a, y)
            single_pass = False
        else:
            yf = scipy.signal.filtfilt(b, a, y)    
    ax.plot(x, yf, label=label, linestyle=ls, linewidth=2)

ax.set_xlabel("time")
ax.legend()
ax.set_xlim(2,5)
ax.set_ylim(-1.5,1.5)

The amplitude of the single pass lfilter (yellow) is comparable to the filtfilt with the corrected cutoff f0/0.8 (red).

On python3.7, Scipy 1.1

[getzze]

@Xurotash So the CORRECT corrected cutoff frequency is: f_corr = fs/pi * arctan( tan(pi*f_c/fs) / C) with C = (2**(1/n) - 1)**(1/4) , n number of passes, fs the sampling frequency and f_c the wanted cutoff frequency. Tested with scipy.signal.butter(2, f_corr/(fs/2)) it gives me the same result as rewriting butter with a correction factor. When f_c << fs/2, the correct correction is almost equal to the wrong correction (f_c/C), so it was not an error easy to spot!

[Xurotash]

I dug some deeper into this cutoff correction, and realised that the correction factor should NOT be applied directly on the cutoff frequency, i.e. f_c_low = f_wanted / C is incorrect. I find this so interesting that i wrote an article on codeproject to highlight this issue. Multi-Pass Filter Cutoff Correction