Question

The unit sample response of Hilbert transform is _______________

(a) Zero

(b) Symmetric

(c) Anti-symmetric

(d) None of the mentioned

I got this question in quiz.

I'd like to ask this question from Design of Hilbert Transformers in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (c) Anti-symmetric

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

Thus from the above equation, we can tell that h(n)=-h(-n). Thus the unit sample response of Hilbert transform is anti-symmetric in nature.