I would like to perform Autocorrelation on the signal shown below. The time between two consecutive points is 2.5ms (or a repetition rate of 400Hz).
This is the equation for estimating autoacrrelation that I would like to use (Taken from http://en.wikipedia.org/wiki/Autocorrelation, section Estimation):
What is the simplest method of finding the estimated autocorrelation of my data in python? Is there something similar to
from numpy import *
import numpy as N
import pylab as P
fn = 'data.txt'
x = loadtxt(fn,unpack=True,usecols=)
time = loadtxt(fn,unpack=True,usecols=)
n = len(x)
variance = x.var()
x = x-x.mean()
r = N.correlate(x, x, mode = 'full')[-n:]
#assert N.allclose(r, N.array([(x[:n-k]*x[-(n-k):]).sum() for k in range(n)]))
result = r/(variance*(N.arange(n, 0, -1)))
I don't think there is a NumPy function for this particular calculation. Here is how I would write it:
def estimated_autocorrelation(x): """ http://stackoverflow.com/q/14297012/190597 http://en.wikipedia.org/wiki/Autocorrelation#Estimation """ n = len(x) variance = x.var() x = x-x.mean() r = np.correlate(x, x, mode = 'full')[-n:] assert np.allclose(r, np.array([(x[:n-k]*x[-(n-k):]).sum() for k in range(n)])) result = r/(variance*(np.arange(n, 0, -1))) return result
The assert statement is there to both check the calculation and to document its intent.
When you are confident this function is behaving as expected, you can comment-out the
assert statement, or run your script with
python -O. (The
-O flag tells Python to ignore assert statements.)