How Do You Calculate the Average Power of a Non-Periodic Signal?

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SUMMARY

The average power of a non-periodic signal can be calculated using the integral of the squared signal over a specified time interval. Specifically, for a non-correlated Gaussian signal, the formula is given by 1/(T2-T1) ∫(T1 to T2) |x(t)|² dt. Understanding the power spectrum, which is the Fourier transform of the autocorrelation function, is crucial for this calculation. Recommended texts for further reading include "Probability, Random Variables, and Stochastic Processes" by Papoulis and "Information, Transmission, Modulation and Noise" by Schwartz.

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  • Understanding of Fourier transforms
  • Familiarity with autocorrelation functions
  • Basic knowledge of Gaussian signals
  • Experience with integral calculus
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Electrical engineers, signal processing specialists, and researchers working with random signals and power calculations will benefit from this discussion.

Apteronotus
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Hi,

I'm wondering how do we calculate the average Power of a random (non-periodic) signal.

I know how to do it if the signal is periodic, but with a non-correlated Gaussian signal I'm a bit lost. Can anyone shed some light?

Thanks,
 
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It's not so simple...rather complex math...The power spectrum ( or spectral density) of a process is the Fourier transoform of its autocorrelation. I was barely able to remember enough to find that so I can't help much further.

One former text is Probability,Random Variables, and Stochastic Processes by Papoulis.
Another one that might help is Information,Transmission, Modulation and Noise, Schwartz.
These are old but may still be available in more current editions.
 
If you've measured the signal as a function of time x(t), you just need to evaluate

\frac{1}{T_2-T_1}\int_{T_1}^{T_2}|x(t)|^2\,dt​

Is that not what you meant?
 
Is the impedance of the circuit constant? Can you average E^2/R?
 

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