# Cross-correlation function problem

1. ## Cross-correlation function problem

Hello everyone,

I have a following problem:

given cross-correlation function $3{C_{12}}{\left(\tau\right)}$ associated with a pair of time functions $3{f}_{1}(t)$ and $3{f}_{2}(t)$:

$3{C_{12}}{\left(\tau\right)}={3cos}^{2}{\sigma}{tsin}{\sigma}{t}$

if $3{f}_{1}(t)=\frac{1}{2}+\frac{1}{4}cos{\sigma}t+\frac{1}{2}sin2{\sigma}t-\frac{3}{2}sin3{\sigma}t+4cos4{\sigma}t$

find $3{f}_{2}(t)$.

The idea I thought of is to apply Fourier transform to cross-correlation function and to the first time function to evaluate spectrum of the second function and then obtain the function

itself by applying inverse Fourier transform to the spectrum. But I didn't manage to do it technically. I believe it has a simple solution like comparison of two time series, say by applying

trigonometric relations to cross-correlation function we have: $3{C_{12}}{\left(\tau\right)}=\frac{3}{2}+\frac{3}{4}sin{\sigma}t+\frac{3}{4}sin3{\sigma}t$. Then it can be

assumed that the second function should include some DC and two waveforms with frequencies of σ and 3σ, but again I don't know how to solve it technically.

Unfortunately I have no answer to the problem, so please could anyone help me to solve it?

•

2. ## Re: Cross-correlation function problem

Can you try solve by Matlab program or Mathematical software ? , may must to adapt littlely that eq before calculation.

--[[ ]]--