Filter an array based on density

Question

I have a sample graph like one below.., which I plotted with set of (x,y) values in an array X.

http://bubblebird.com/images/t.png

As you can see the image has dense peak values between 4000 to 5100

My exact question is can I programmatically find this range where the graph is most dense?
ie.. with Array X how can I find range within which this graph is dense?
for this array it would be 4000 - 5100.

Assume that the array has only one dense region for simplicity.
Thankful if you can suggest a pseudocode/code.

Answer 1

You can use the variance of the signal on a moving window. Here is an example (see the graph attached where the test signal is red, the windowed variance is green and the filtered signal is blue) :

:

test signal generation :

import numpy as np
X = np.arange(200) - 100.  
Y = (np.exp(-(X/10)**2) + np.exp(-((np.abs(X)-50.)/2)**2)/3.) * np.cos(X * 10.)

compute moving window variance :

window_length = 30 # number of point for the window
variance = np.array([np.var(Y[i-window_length / 2.: i+window_length/2.]) for i in range(200)])

get the indices where the variance is high (here I choose the criterion variance superior to half of the maximum variance... you can adapt it to your case) :

idx = np.where(variance > 0.5 * np.max(variance))

X_min = np.min(X[idx])
# -14.0
X_max = np.max(X[idx])
# 15.0

or filter the signal (set to zero the points with low variance)

Y_modified = np.where(variance > 0.5 * np.max(variance), Y, 0)