Question

The unit sample response of an ideal Hilbert transform is

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

(b) =0; n=0

(c) True

(d) False

I have been asked this question by my school teacher while I was bunking the class.

My doubt is from Design of Hilbert Transformers topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (a) =\(\frac{2}{\pi} \frac{(sin(\frac{πn}{2}))^{2}}{n}\); n≠0

The best explanation: We know that the frequency response of an ideal Hilbert transformer is given as

H(ω)= -j ;0 < ω < π

j ;-π < ω < 0

Thus the unit sample response of an ideal Hilbert transform is obtained as

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

h(n)=0; n=0