Question

Consider the continuous-time (analog) signal x a ​ (t)=kte −β∣t∣ , where k=4000. (a) Assuming that the energy of the signal x a ​ (t) is 90 , determine the value of β.

Answer 1

To determine the value of β in the signal equation x(t) = kte^(-β|t|), use the energy of the signal and integrate the squared magnitude over its duration.

Step-by-step explanation:

To determine the value of β in the continuous-time signal equation x(t) = kte^(-β|t|), we need to use the energy of the signal. Given that the energy of the signal is 90, we can calculate β.

The energy of the signal can be found by integrating the squared magnitude of the signal over its entire duration.

∫(kte^(-β|t|))^2dt = 90

Simplifying the equation and evaluating the integral leads to the value of β.

4000β = 90, so β = 90/4000 = 0.0225.