Let's consider an example where you calculate the autocorrelation function for an electrical signal in a circuit. The autocorrelation function is widely used in signal processing and communications to analyze how a signal correlates with itself at different time lags.

Example: Autocorrelation of a Voltage Signal in a Circuit

Suppose we have a periodic voltage signal in an electrical circuit given by the following function:

$V(t)=A*sin(2ft)$

Where:

$A$ is the amplitude of the voltage $($say$,A=10V).$

$f$ is the frequency of the signal $($say$,f=60Hz),$

$t$ is time.

We want to compute the autocorrelation function $R()$ of this signal, where $$ is the time lag.