# Correlation confused on integration

1. Mar 14, 2014

### cutesteph

x(n)=exp(i(x*n+theta1)) +exp(i(y*n+theta2)) x and y are constants , theta1, theta2 are uniform random on [0,2*pi]

R(f) =E[{ exp(i(x*n+theta1)) +exp(i(y*n+theta2)) }exp(-i(x*(n-f)+theta1)) +exp(-i(y*(n-f)+theta2)) }]
= 4 products 2 of which will be similar but with the opposite constants

E[exp(i*x*n+i*theta1 -i*x*n+i*n*f0i*theta1] = E[exp(i*x*f)] =integral exp(i*x*f) dtheta1 0 to 2 pi = 2*pi*exp(i(x*f)
Or am I suppose to integral over both theta1 and theta 2 to get 4*pi*exp(i*x*f) ?

E[exp(i*n*n+i*theta1 -i*y*n +i*y*f- i*theta2 ] = double integral of the inside but it equals zero since we can separate the exponential and get exp(i*theta1) and the integral of this over 0 2pi = 0.
Right?

2. Mar 15, 2014

### micromass

You're gonna get much more responses if you learn LaTeX. It'll make your posts way more readable. Read this: https://www.physicsforums.com/showpost.php?p=3977517&postcount=3

Anyway, because jbunniii asked me to:

Last edited: Mar 15, 2014
3. Mar 15, 2014

### mathman

There seem to be some typos in the formulas, which make it difficult to understand what is being presented.