In an electrical system with a resistor, voltage and current signals facilitate the measurement of power and energy across the resistor. For a continuous-time signal, the total energy over a time interval is defined as the integral of the square of the signal's magnitude over that interval. Mathematically, this is expressed as:

The time-averaged power is calculated by dividing the total energy by the duration of the time interval, given by:

For a discrete-time signal, the total energy is computed by summing the squares of the signal's magnitude for all points within the interval:

The average power is found by dividing the total energy by the number of points in the interval:

These expressions for total energy and power are redefined for infinite time intervals to accommodate practical applications.

Based on these definitions, signals are categorized into three types: energy signals, power signals, and non-physical signals. Energy signals have finite total energy, resulting in zero average power. Conversely, power signals have finite average power, leading to infinite total energy over an infinite interval. Non-physical signals are those where neither power nor energy is finite, making them impractical for real-world applications. Understanding these classifications is vital for accurate signal analysis and efficient energy management in electrical systems.