Question

The magnitude function |H(ω)| can be zero at some frequencies, but it cannot be zero over any finite band of frequencies.

(a) True

(b) False

This question was posed to me in examination.

I'm obligated to ask this question of General Considerations for Design of Digital Filters topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (a) True

Best explanation: One important conclusion that we made from the Paley-Wiener theorem is that the magnitude function |H(ω)| can be zero at some frequencies, but it cannot be zero over any finite band of frequencies, since the integral then becomes infinite. Consequently, any ideal filter is non-causal.