Question

The unit sample response of Hilbert transform is infinite in duration and causal.

(a) True

(b) False

This question was posed to me in exam.

This question is from Design of Hilbert Transformers in division Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (b) False

Explanation: We know that the unit sample response of the Hilbert transform is given as

h(n)=\(\frac{2}{\pi} \frac{(sin(\frac{πn}{2}))^{2}}{n}\); n≠0

h(n)=0; n=0

it sample response of an ideal Hilbert transform is infinite in duration and non-causal.