Question

As the value of the frequency Ω tends to ∞, then |H(jΩ)| tends to ____________

(a) 0

(b) 1

(c) ∞

(d) None of the mentioned

The question was posed to me during an interview.

My question comes from Butterworth Filters topic in division Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (a) 0

For explanation I would say: We know that the magnitude frequency response of a Butterworth filter of order N is given by the expression

|H(jΩ)|=\(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

In the above equation, if Ω→∞ then |H(jΩ)|→0.