Question

If |H(ω)| is square integrable and if the integral \(\int_{-\pi}^\pi |ln⁡|H(ω)||dω\) is finite, then the filter with the frequency response H(ω)=|H(ω)|e^jθ(ω) is?

(a) Anti-causal

(b) Constant

(c) Causal

(d) None of the mentioned

I have been asked this question during an interview.

I need to ask this question from General Considerations for Design of Digital Filters topic in division Digital Filters Design of Digital Signal Processing

Answer 1

Correct option is (c) Causal

The explanation is: If |H(ω)| is square integrable and if the integral \(\int_{-\pi}^\pi |ln⁡|H(ω)||dω\) is finite, then we can associate with |H(ω)| and a phase response θ(ω), so that the resulting filter with the frequency response H(ω)=|H(ω)|e^jθ(ω) is causal.