Final answer:
Signal t^2 is neither a power signal nor an energy signal since its energy and power are unbounded. Similarly, signal |t| is also not an energy signal as it contains infinite energy.
Step-by-step explanation:
The energy and power classification of signals is an important concept in engineering, particularly in signal processing and communication systems. To determine if a signal is an energy signal or a power signal, one needs to evaluate the signal's properties over time.
Energy Signals
Energy signals have finite energy, which can be calculated using the formula:
E = ∫ |x(t)|^2 dt
Where E represents the energy of the signal and x(t) is the signal itself. An energy signal has finite energy and zero power in the limit as time approaches infinity.
Power Signals
On the other hand, a power signal has finite power, which is defined as:
P = lim_{T→∞} 1/(2T) ∫_{-T}^{T} |x(t)|^2 dt
Where P is the average power and T is the period of the signal. A power signal has finite power and possibly infinite energy.
Determining Signal Types
To determine if t^2 is a power signal, we would attempt to calculate the above average power limit. However, we can already see that the energy of the signal over time is unbounded, and the average power will also be infinite, therefore it is neither a power signal nor an energy signal. On the other hand, |t| considered over all time spans also contains infinite energy, making it not an energy signal either.