Correlation

Correlation is a measure of similarity between two signals. The general formula for correlation is

∫∞−∞x1(t)x2(t−τ)dt$${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{x}_1(t)x_2(t-\tau )dt$$

There are two types of correlation:

• Auto correlation
• Cros correlation

Auto Correlation Function

It is defined as correlation of a signal with itself. Auto correlation function is a measure of similarity between a signal & its time delayed version. It is represented with R(τ$\tau$).

Consider a signals x(t). The auto correlation function of x(t) with its time delayed version is given by

R11(τ)=R(τ)=∫∞−∞x(t)x(t−τ)dt[+ve shift]$$R_{11}(\tau )=R(\tau )={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}x(t)x(t-\tau )dt\text{[+ve shift]}$$

=∫∞−∞x(t)x(t+τ)dt[-ve shift]$$={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}x(t)x(t+\tau )dt\text{[-ve shift]}$$

Where τ$\tau$ = searching or scanning or delay parameter.