python - How to get high and low envelope of a signal?

Question

I have quite a noisy data, and I am trying to work out a high and low envelope to the signal. It is kinda of like this example in MATLAB:

http://uk.mathworks.com/hel

Answer 1

Building on @A_A 's answer, replace the sign check with nim/max test to make it more robust.

import numpy as np
import scipy.interpolate
import matplotlib.pyplot as pt
%matplotlib inline

t = np.multiply(list(range(1000)), .1)
s = 10*np.sin(t)*t**.5

u_x = [0]
u_y = [s[0]]

l_x = [0]
l_y = [s[0]]

#Detect peaks and troughs and mark their location in u_x,u_y,l_x,l_y respectively.
for k in range(2,len(s)-1):
    if s[k] >= max(s[:k-1]):
        u_x.append(t[k])
        u_y.append(s[k])

for k in range(2,len(s)-1):
    if s[k] <= min(s[:k-1]):
        l_x.append(t[k])
        l_y.append(s[k])

u_p = scipy.interpolate.interp1d(u_x, u_y, kind = 'cubic', bounds_error = False, fill_value=0.0)
l_p = scipy.interpolate.interp1d(l_x, l_y, kind = 'cubic', bounds_error = False, fill_value=0.0)

q_u = np.zeros(s.shape)
q_l = np.zeros(s.shape)
for k in range(0,len(s)):
    q_u[k] = u_p(t[k])
    q_l[k] = l_p(t[k])

pt.plot(t,s)
pt.plot(t, q_u, 'r')
pt.plot(t, q_l, 'g')

If you expect the function to be increasing, try:

for k in range(1,len(s)-2):
    if s[k] <= min(s[k+1:]):
        l_x.append(t[k])
        l_y.append(s[k])

for the lower envelope.