- #1
drkidd22
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Homework Statement
x(t) = e(-2t) * u(t)
Ex = x2(t) dt
Attached is the work I have done. Got stuck towards the end.
The formula for calculating the energy of a signal is E = ∫x(t)^2 dt, where x(t) represents the signal and the integral is taken over the entire time domain.
For a signal with a time-dependent amplitude, the energy can be calculated by first finding the squared magnitude of the signal at each time point, and then integrating this over the entire time domain. In other words, the formula becomes E = ∫|x(t)|^2 dt.
In this signal, "e" represents the mathematical constant known as Euler's number, which is approximately equal to 2.71828. The significance of "e" is that it is often used to model exponential growth and decay, making it a useful tool in signal analysis.
The unit step function u(t) serves as a switch that turns the signal on at t = 0 and keeps it off for all negative values of t. This ensures that the signal only exists and has a non-zero value for t ≥ 0, making it a causal signal.
No, the energy of a signal can never be negative. This is because the energy is calculated by squaring the magnitude of the signal, which will always result in a positive value. In addition, physical signals cannot have negative energy, as it would violate the law of conservation of energy.