1.

What is the frequency response of a Hilbert transform H(F)=?(a) \(\begin{cases}&-j(F>0) \\ & 0(F=0)\\ & j(F0)\\0 &(F=0) \\j & (F0)\\0 & (F=0)\\j & (F

Answer»

Correct choice is (a) \(\begin{cases}&-j(F>0) \\ & 0(F=0)\\ & j(F<0)\end{cases}\)

For explanation I would say: H(F) =\(\int_{-∞}^∞ h(t)E^{-j2πFt} dt\)

=\(\frac{1}{π} \int_{-∞}^∞ 1/t e^{-2πFt} dt\)

=\(\left\{\begin{MATRIX}-j& (F>0)\\0&(F=0) \\ j& (F<0)\end{matrix}\right.\)

We Observe that │H (F)│=1 and the PHASE response &odot;(F) = -1/2π for F > 0 and &odot;(F) = 1/2π for F < 0.



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