If G(t) is Hilbert transform of g(t), then G(t) is:

Question

TuteeHUB · Accepted Answer

$ - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau $

TuteeHUB · Answer

$ - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{ - g\left( \tau \right)}}{{t - \tau }}d\tau $

TuteeHUB · Answer

$ - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^0 \frac{{ - g\left( \tau \right)}}{{t - \tau }}d\tau $

TuteeHUB · Answer

$\frac{1}{\pi }\mathop \smallint \limits_0^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau $

1.	If G(t) is Hilbert transform of g(t), then G(t) is:
A.	\( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{ - g\left( \tau \right)}}{{t - \tau }}d\tau \)
B.	\( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau \)
C.	\( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^0 \frac{{ - g\left( \tau \right)}}{{t - \tau }}d\tau \)
D.	\(\frac{1}{\pi }\mathop \smallint \limits_0^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau \)
Answer» B. \( - \frac{1}{\pi }\mathop \smallint \limits_{ - \infty }^\infty \frac{{g\left( \tau \right)}}{{t - \tau }}d\tau \)

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