Energy (signal processing)

In a power signal is in the signal theory to a real - or complex-valued signal s ( t) with finite signal energy.

Definition of continuous signals

A complex-valued continuous signal s is said to be energy signal if:

For purely real values ​​, the equation simplifies to

Definition for discrete signals

A complex-valued discrete signal s is called energy signal if:

In a purely real-valued discrete signals s applies accordingly:

As usual, was called the conjugate of complex number s. The value of each integral or the respective sum is called signal energy.

Typical energy signals

Typical energy signals are the signals which represent the finite signal values ​​and will eventually be turned on and off. Notable examples are decaying or individual, time-limited pulses.

Typical non-energy signals are all power signals. A special place in the theory assumes a Dirac pulse, which is also not an energy signal. The integral of the function signal does not result in the normalized value of 1, but the integral of the square of the signal function.

Physical background

The signal processing is based on the concepts of physics and electrical engineering. Is considered as a signal, for example, a current i flowing through a resistor R, then the instantaneous power calculated

And correspondingly the total energy converted to

Theoretical background signal

Signal theory is the amount of energy signals with the addition of functions and multiplication by a real or complex number a vector space with an infinite number of basis vectors. As base vectors are in particular sine and cosine functions into consideration. The Fourier transformation is the essential element of equipped with these basis vectors vector or signal space.