We can find in standard textbooks the formula for finding the autocorrelation function of the response of a system to a white Gaussian noise. This formula contains a term S0 which denotes the PSD of the white noise. How can I plot the autocorrelation function ? Isn't the PSD of white noise infinite ?
The autocorrelation function of a white noise signal is the Dirac delta distribution. Its plot would be a line at frequency 0. The unit delta distribution represents a signal with unit energy.
Peter Russer is right. If it is truly white noise... If it is not, then the 'whiteness' can be assessed by comparing what you do obtain with what the theory says you would obtain. This is the usefulness of it.
Hello, thank you for answering.I am not trying to plot the autocorrelation function for white noise, I am trying to plot the autocorrelation function of the response to white noise.
Ahhhh... I see! The response to white noise will be an interesting characteristic of your system. It will allow you to assess its frequency response.
If you are interested in the autocorrelation function of the response to white noise you have to convolve the input function with the transfer function to obtain the output function. Since the white noise input function is described by the delta distribution and the convolution with the delta distribution is an identity operation, the autocorrelation function of the output signal will be the autocorrelation function of the transfer function.
Professor Russer, I would be extremely grateful if you could clarify one issue.Autocorrelation function for Tau = 0 is nothing but E[ |n(t)|2 ]. Please correct me if wrong. So this value is the variance of the noise function . But for a gaussian random variable for each instant of time , as is the description of white noise, this is a finite value and not an impulse, as opposed to how the psd comes out to be. Please help
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