Why Do We Use Squaring Instead of Absolute Value in Signal Power Calculations?

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Discussion Overview

The discussion revolves around the methods of calculating energy and power in signals, specifically questioning the use of squaring the signal versus taking the absolute value before integration. Participants explore the implications of these methods and the physical significance of distinguishing between power and energy signals.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question why the absolute value of a signal is not used for energy and power calculations, suggesting that integrating the absolute value might yield similar results to integrating the squared signal.
  • There is a query regarding the physical significance of determining whether a signal is classified as power or energy, and what additional information these classifications provide beyond periodicity.
  • One participant seeks clarification on whether the integration pertains to voltage, current, or power, indicating a potential misunderstanding of the terms used in signal processing.
  • Another participant points out that integrating an AC voltage or current signal over an infinite range results in zero, which raises concerns about the appropriateness of the integration limits in these calculations.
  • This participant explains the utility of Mean Square or Root Mean Square methods, noting that they provide average power without needing to integrate the product of voltage and current directly, which can be zero due to sign changes in AC signals.
  • There is a mention of the relationship between power and resistance, emphasizing that power calculations typically focus on average values over specific time intervals rather than infinite limits.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using absolute values versus squaring in calculations, and there is no consensus on the best approach. The discussion remains unresolved regarding the implications of these methods and their physical significance.

Contextual Notes

Some assumptions about the definitions of energy and power in the context of signals may be missing, and the discussion does not fully address the implications of integrating over infinite limits versus finite intervals.

LLT71
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in terms of calculating energy and power, why don't we use absolute value of signal and then integrate it from -inf to +inf instead of squaring it and then integrating it over -inf to +inf?
for example ∫|sinx|dx (from -inf to +inf) will give you, relatively speaking, the same answer as ∫[sinx]^2dx (from -inf to +inf).

what is physical significance of determining if signal is power or energy one? what those two quantities tell you besides if signal is periodic/non-periodic?
 
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LLT71 said:
in terms of calculating energy and power, why don't we use absolute value of signal and then integrate it from -inf to +inf instead of squaring it and then integrating it over -inf to +inf?
for example ∫|sinx|dx (from -inf to +inf) will give you, relatively speaking, the same answer as ∫[sinx]^2dx (from -inf to +inf).

what is physical significance of determining if signal is power or energy one? what those two quantities tell you besides if signal is periodic/non-periodic?
Are you integrating voltage, current or power?
 
berkeman said:
Are you integrating voltage, current or power?
please sorry in advance for my ignorance! in my Signal Processing textbook it says that for every continuous signal we define energy of signal as ∫|[x(y)^2]|dx so, since I'm new at this I presume it stands for "any signal".
 
A couple of points here. If you integrate (+-∞) an AC Voltage or Current signal, the result is Zero.
The reason for using Mean Square or Root Mean Square is that you very seldom have both V and I signals available. RMS gives you the (Average) Power that your Voltage waveform will dissipate in a resistive load without Integrating VI (which is not zero because both signs change at the same time to produce positives for each half of the cycle).
Power = V2R or I2R, whichever you choose or can measure.
We normally deal with Power, in these cases and that is the Average over a specific time (a number of whole cycles of the waveform ). So your Integration is not +-∞.
 
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