# when to use auto correlation and when to use fourier transform

In communication, if we don't know any prior information about the signal, we perform an auto correlation say Rx(T) and take the Fourier transform of Rx(T) to analyze the power spectrum.

Supposing if my signal is known do i need to perform auto correlation , or simply i can take a Fourier transform, and then calculate the power from it.?

Am I seeing it right? or am I missing something here.?

• If you don't find an adequate answer here, you might also try DSP. A similar question might even already have an answer over there. – The Photon Oct 22 '14 at 16:18

$$R_x(\tau)=\int_{-\infty}^{\infty}x(t)x(t-\tau)dt=x(t)*x(-t)$$
where $*$ denotes convolution. Noting that the Fourier transform of $x(-t)$ is $X(-\omega)=X^*(\omega)$ (because $x(t)$ is real-valued), you get for the Fourier transform of the autocorrelation
$$\mathcal{F}\{R_x(\tau)\}=X(\omega)X^*(\omega)=|X(\omega)|^2$$