13.3:
Energy and Power Signals
Consider an electric system with a resistor. Here, the voltage and current signals enable power and energy measurement across the resistor.
For a continuous-time signal, the total energy over the time interval is defined as the integral of the square of the signal's magnitude over the same interval.
The time-averaged power is calculated by dividing the total energy by the duration of the time interval.
For a discrete-time signal, the total energy over the time interval is computed by summing the squares of the signal's magnitude for all points within the interval, while the average power is found by dividing the total energy by 2N+1.
The expressions for total energy and power are redefined for continuous and discrete signals over the intervals —t1 to t2 and –n1 to n2.
Based on these definitions, there are three major types of signals.
Energy signals have finite total energy, resulting in zero average power.
Power signals have finite average power, which results in infinite energy.
Non-physical signals are signals where neither power nor energy are finite.
13.3:
Energy and Power Signals
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.