# Integral relation for Wiener-Khintchine theorem

1. Feb 14, 2008

### brendan_foo

Hi folks,

I am just looking for a leg up in completing the Wiener-Khintchine theorem. Most of it seems rudimentary, however, to finish this off I must get over the hurdle that is:

$$\int_{-T}^{T} \int_{-T}^{T} x(t - \tau) dt d\tau = \int_{-2T}^{2T} (2T - |\tau|)x(\tau)d\tau$$

I thought that I could show this by some pictorial argument (that is, by showing some obvious relations of the area and function shifts, similar to a convolution) but I'm not sure that this is satisfactory to harness my knowledge of the step. Could anyone suggest the first step of analytical reasoning or a nudge in the right direction?

Cheers...
Brendan

Last edited: Feb 14, 2008