When given a discrete impulse response, let us say it is from an FIR filter so it is finite, how can I assume the filter type? The task is to recognize or to preclude one or more of the following types:
- Low pass
- High pass
- Band stop
- Band pass
For example, I read that a zero at $h(n = 0)$ (where h is the impulse response of my filter) means that the filter is a low pass but how can I say that with precluding the band stop immediately?