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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 mentionedI 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»

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.



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