Cross term gives the autocorrelation?

[SamTaylor]

I am reading a research paper about "narrow" autocorrelation and
at the beginning there is an expression I don't unterstand

The autocorrelation function is defined as the product
$$g(\tau) = \int\limits_{-\infty}^\infty f(t) \cdot f(t-\tau) dt$$
It is convenient to calculate this as $$<|f(t) + f(t-\tau)|^2>$$,
where the cross term gives the autocorrelation.

http://www.wellesley.edu/Physics/brown/pubs/acv85_P1595-P1601.pdf"

Does someone know what is meant with the word cross term?

 

[mathman]

When you expand (a+b)², it becomes a² +2ab +b².

The term 2ab is the cross term. What you want is gotten by expanding the integrand to get 3 integrals and using the middle one, omitting the 2.

 

[SamTaylor]

Thanks