Final answer:
The given signal x(t) = (1/t)[u(t-1)-u(t-2)] can be represented as a waveform by breaking it down into two step functions, u(t-1) and u(t-2). The energy and average power of the signal can be determined by evaluating the integrals of |x(t)|^2 over the interval [0, ∞).
Step-by-step explanation:
The given signal is x(t) = (1/t)[u(t-1)-u(t-2)].
To draw the waveform, we can break it down into two step functions: u(t-1) and u(t-2). The step function u(t-a) is equal to 1 when t >= a, and 0 otherwise.
Using this information, we can plot the waveform as follows:
- At t < 1, x(t) = 0 since u(t-1) and u(t-2) are both 0.
- At 1 <= t < 2, x(t) = 1/t since u(t-1) = 1 and u(t-2) = 0.
- At t >= 2, x(t) = 0 since u(t-1) and u(t-2) are both 1.
The energy of a signal x(t) over the interval T is given by E = ∫|x(t)|^2 dt. To find the energy of this signal, we need to calculate the integral of |x(t)|^2 over the interval [0, ∞)
The average power of a signal x(t) over the interval T is given by P_avg = (1/T)∫|x(t)|^2 dt. To find the average power of this signal, we need to calculate the integral of |x(t)|^2 over the interval [0, ∞) and divide it by the total time period T.
By evaluating the integrals, we can find the energy and average power of the signal.