Question

Determine the values of P. and E. for each of the following signals:
x1(t) = e⁻²ᵗ u(t)

Answer 1

The given signal is x1(t) = e^-2t u(t), where e is Euler's number, t represents time, and u(t) is the unit step function. To determine the values of P and E for this signal, separate it into its magnitude and phase components using Euler's formula. In this case, the magnitude decreases exponentially with time, while the phase remains constant at zero.

Step-by-step explanation:

The given signal is x1(t) = e-2tu(t). In this expression, e is Euler's number, t represents time, and u(t) is the unit step function.

To determine the values of P and E for this signal, we need to separate it into its magnitude and phase components. Using Euler's formula, we can rewrite the signal as x1(t) = |P|e^(jE)t, where P is the magnitude and E is the phase.

In this case, |P| = e-2t and E = 0. We can see that the magnitude decreases exponentially with time, while the phase remains constant at zero.