# duration for a signal after filtering [duplicate]

I have a signal $$s(t)$$ of duration $$T$$. This signal doesn't have a limited bandwidth. To solve this problem, I filter it with a pulse shaping filter (raised cosine filter).

My question: Does filtering change the duration of the signal?

## 1 Answer

A classical result states that a (non-trivial) time-limited signal does not have a limited bandwidth (in terms of support). The converse happens as well: a bandwidth-limited signal cannot be of finite length.

And there is a similar rule-of-thumb principle: when you try to reduce the support of a signal in one domain (time or frequency), you generally spread it in the other domain.