In general, I know that the impulse response $h(t)$ of an LTI system can be complex. However, all of physically realizable, useful systems I've come across have purely real impulse responses. I did a web search in an attempt to find a useful, non-pathological system with a complex impulse response, but was not immediately successful.
Could anyone provide an example of a system with a complex impulse response, and state what applications it has? Links to such examples would also be appreciated.