Question

Determine the average power of the following signals: (a) f(t) = sin^4(t) (same as in 3a) (b) f(t) = e^t for -π ≤ t < π, with period T = 2π s (same as in 3b)

a) Same
b) Different
c) Cannot be determined
d) Period not given

Answer 1

The average power for signal (a) sin^4(t) would typically be calculated using integral calculus, but cannot be fully determined here. For signal (b) e^t, the exponential nature makes the calculation of average power non-standard, and it cannot be determined using typical sinusoidal wave formulas.

Step-by-step explanation:

The question asks us to determine the average power of two different signals. To do this, we need to understand the relationship between power, amplitude, frequency, and period in wave mechanics.

For signal (a), f(t) = sin^4(t), to find the average power we need the square of the amplitude and the square of the angular frequency, which requires us to perform some integral calculus over one period to find the average value of the square of the given function.

For signal (b), f(t) = e^t over the interval -π ≤ t < π, with a period T = 2π s, is not a typical periodic function and does not conform to normal sinusoidal wave equations. While the period is given, this function increases exponentially, and therefore its power cannot be averaged using standard wave formulas over a period.

The correct response for the average power of the signals, considering the information provided, cannot be determined without further calculations that are not demonstrated here.