Power signal

In a power signal is in the signal theory to a real- or complex-valued signal s (t) with infinite signal energy , but finite average power . Formally this means:

${\displaystyle 0<P=\lim \limits _{T\to \infty }{{\frac {1}{2T}}\int \limits _{-T}^{T}{s(t)\cdot s^{*}(t)dt}}<\infty \ .}$

The asterisk means the complex conjugation of the function s (t).

In the case of real-valued signals, this corresponds to the requirement

${\displaystyle 0<P=\lim \limits _{T\to \infty }{{\frac {1}{2T}}\int \limits _{-T}^{T}{s(t)^{2}dt}}<\infty \ .}$

The instantaneous power of real signals at time t is calculated as follows:

${\displaystyle P(t)=\lim \limits _{T\to 0}{{\frac {1}{2T}}\int \limits _{t-T}^{t+T}{|s(t)|^{2}dt}}=|s(t)|^{2}\ .}$

Typical power signals are periodically continued energy signals such as a sine signal or a cosine signal and stochastic signals ( noise ).

No power signals are, for example, all energy signals, signals that grow exponentially over all limits or even the function . ${\displaystyle s(t)={\frac {1}{t}}}$

literature

• Hans Dieter Lüke: Signal transmission . 6th edition. Springer Verlag, 1995, ISBN 3-540-54824-6 .
• Werner Rupprecht: Signals and transmission systems. Models and processes for information technology, Springer Verlag, Berlin / Heidelberg 1993, ISBN 978-3-540-56853-7 .
• Karl Steinbuch, Werner Rupprecht: communications engineering. Volume II Communication, 3rd edition, Springer Verlag, Berlin / Heidelberg 1982, ISBN 978-3-540-11352-2 .
• Uwe Kiencke, Michael Schwarz, Thomas Weickert: Signal processing. Time-frequency analysis and estimation method, Oldenbourg Verlag, Munich 2008, ISBN 978-3-486-58668-8 .

Web links

• Energy signals and power signals (accessed July 20, 2018)
• Discrete-time signals (accessed July 20, 2018)
• Signals and Systems (accessed July 20, 2018)