0
$\begingroup$

I have this sentence in a report but I don't quiet know what it means. I am familier with covariance and covariance matrices but not with covariance functions.

$f(t)$ is a continuous-time white-noise process with zero mean and the covariance function $\mathbb{E}f(t)f(s)^\top = R \delta(t − s)$.

My guess is is that the $f(t)$ actually has a covariance matrix of $R$, but what is with the $\delta(t - s)$? With $\delta$ being the delta function I guess?

$\endgroup$
1
$\begingroup$

Yes, it's the delta function. The formula means that for every $t$ the variable $f(t)$ has variance $R$ and for every $s\neq t$ variables $f(s)$ and $f(t)$ are uncorrelated. This corresponds to the more intuitve discrete-time white noise.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.