Question

The system under consideration is an RC low-pass filter with R = 1 kΩ and C = 1 µF. Let H (f) denotes the frequency response of the RC, low-pass filter. Let t1(f) be the group delay function of the given RC low-pass filter and f2 = 100 Hz. Then tg(f2) in ms is ___________

(a) 0.717

(b) 7.17

(c) 71.7

(d) 4.505

The question was asked during an interview.

Question is from Region of Convergence topic in chapter Laplace Transform and System Design of Signals and Systems

Answer 1

Correct choice is (a) 0.717

Easy explanation: H (ω) = \(\frac{1}{1+jωRC}\)

Now, θ (ω) = – tan^-1(ωRC)

Group delay = tg (ω) = – \(\frac{d θ(ω)}{dω}\)

= – \(\frac{d tan^{-1} (ωRC)}{dω}\)

∴ tg (ω) = \(\frac{RC}{1+ω^2 R^2 C^2}\)

Now, tg (f) = \(\frac{RC}{1+4π^2 f^2 R^2 C^2}\)

So, tg (f2) = \(\frac{RC}{1+4π^2 f_2^2 R^2 C^2}\) = 0.717 ms.