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HR(ω) and HI(ω) are interdependent and cannot be specified independently when the system is causal.

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in Digital Signal Processing by (829k points)
HR(ω) and HI(ω) are interdependent and cannot be specified independently when the system is causal.

(a) True

(b) False

I had been asked this question by my school principal while I was bunking the class.

Origin of the question is General Considerations for Design of Digital Filters in chapter Digital Filters Design of Digital Signal Processing

1 Answer

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The correct answer is (a) True

The best I can explain: Since h(n) is completely specified by he(n), it follows that H(ω) is completely determined if we know HR(ω). Alternatively, H(ω) is completely determined from HI(ω) and h(0). In short, HR(ω) and HI(ω) are interdependent and cannot be specified independently when the system is causal.

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