Wednesday, 13 March 2013

Periodic signals are power signals

Periodic signals are power signals; nonperiodic signals (pulses) are energy signals. When both power and energy are infinite, the signal is neither a power nor an energy signal. As a matter of fact, a true power signal cannot exist in the real world because it would require a power source that operates for an infinite amount of time

ENERGY SIGNAL

Some signals qualify to be classified as energy signals, whereas some other signals qualify to be classified as power signals. Given a continuous-time signal f(t), the energy contained over a finite time interval is defined as follows.
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Equation (3.8) defines the energy contained in the signal over time interval from T1 till T2. On the other hand, equation (3.9) defines the total energy contained in the signal. If the total energy of a signal is a finite non-zero value, then that signal is classified as an energy signal. Typically the signals which are not periodic turns out to be energy signals. For example, a single rectangular pulse and a decaying exponential signal are energy signals.



POWER SIGNAL

When a reference to power in a signal is made, it points to the average power. Power is defined as energy per second. For a continuous-time signal, we can obtain an expression for power from equation (3.9).
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Most of the periodic signals tend to be power signals. Given the period of a cycle, the power of a periodic signal can be defined by equation (3.11). Equation (3.11) can be used to find the power of a dc signal also. The dc signal is also a power signal. If power of a signal is a finite non-zero value and its energy is infinite, then that signal is classified as a power signal. There are some signals which can be classified neither as power signals nor as energy signals. For example, a ramp signal defined from zero till infinity is neither a power signal nor an energy signal, since both power and energy of ramp signal is not bounded. But in practice. such a signal cannot exist and hence such a signal is not of any practical importance.


Energy and Power of Signals from the Wolfram Demonstrations Project by Daniel de Souza Carvalho

1 comment:

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