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The unit sample response of Hilbert transform is _______________(a) Zero(b) Symmetric(c) Anti-symmetric(d) None of the mentionedI 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»

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.



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