Question

Visualize a complex exponential signal, e-12πt What is the frequency of the signal? Label the axes clearly. 6. X axis

Answer 1

ANSWER - 6

AS WE KNOW,

SINCE, BOTH COS AND SIN HAVE A TIME PERIOD OF 2$\pi$ in radians and $\omega = 2\pi f$ ; THEREFORE ==>

HERE, $\omega = 2\pi f$ =  $2\pi$

==> f = 1 Hz ==> ANSWER

NOW, x-axis = $cos(2\pi t)$

and y-axis = $-sin(2\pi t)$

Therefore, x² + y² = 1 and his shows a unit circle in x-y plane. You can draw the graph of the unit now on your own. If you need any further help, please write in the comments.

ANSWER - 7

(a) $\delta (0) = \inf\ (By\ definition,\ inf\ means\ infinity)$

(b) By definition, this integral = $\int_{-inf}^{inf}\delta (t).dt = 1$

(c) If t<0, then ==> $\int_{-inf}^{t}\delta (t).dt = 0$

  If t>0, then ==> $\int_{-inf}^{t}\delta (t).dt = 1$

If t=0, then ==> $\int_{-inf}^{t}\delta (t).dt = 0.5$

All the above answers come from the definition only.

Please write in the comments, if you need any further help.