Signal energy and RC circuitThe signal x(t) = e £t £ is defined for all values of

Signal energy and RC circuit€”The signal x(t) = e^{ˆ’ˆ£tˆ£}is defined for all values of t.

(a) Plot the signal x(t) and determine if this signal is finite energy.

(b) If you determine that x(t) is absolutely integrable, or that the following integral

is finite, could you say that x(t) has finite energy? Explain why or why not.

(c) From your results above, is it true the energy E_y of the signal

y(t) = e^ˆ’t cos(2Ï€ t) u(t)

is less than half the energy of x(t)? Explain. To verify your result, use symbolic MATLAB to plot y(t) and to compute its energy.

(d) To discharge a capacitor of 1 mF charged with a voltage of 1 volt we connect it, at time t = 0, with a resistor R. When we measure the voltage in the resistor we find it to be v_R (t) = e^ˆ’t u(t). Determine the resistance R. If the capacitor has a capacitance of 1 μF, what would be R? In general, how are R and C related?

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