Question

If h(n) is the real valued impulse response sequence of an LTI system, then what is the phase of H(ω) in terms of HR(ω) and HI(ω)?

(a) \(tan^{-1}\frac{H_R (ω)}{H_I (ω)}\)

(b) –\(tan^{-1}\frac{H_R (ω)}{H_I (ω)}\)

(c) \(tan^{-1}\frac{H_I (ω)}{H_R (ω)}\)

(d) –\(tan^{-1}\frac{H_I (ω)}{H_R (ω)}\)

I have been asked this question during a job interview.

This is a very interesting question from Frequency Domain Characteristics of LTI System topic in division Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

The correct choice is (c) \(tan^{-1}\frac{H_I (ω)}{H_R (ω)}\)

The best explanation: If h(n) is the real valued impulse response sequence of an LTI system, then H(ω) can be represented as HR(ω)+j HI(ω).

=> tanθ=\(\frac{H_I (ω)}{H_R (ω)}\) => Phase of H(ω)=\(tan^{-1}\frac{H_I (ω)}{H_R (ω)}\)