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When energy is referred to as the square summable sequence, is that energy a representation of the power of the signal? How is the energy of frequency determined?

E.g. what if an audio signal has high energy on the higher frequencies and another has high energy on the lower, bass, frequencies, how is this determined?

What exactly is the power from the square summable series representing then and is it useful for audio?

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No, energy is not the same as power. Power is energy per unit of time. An analogy- energy is like distance, while power is like speed.

The easiest way to determine energy in the frequency domain is to take the signal and do an FFT. The Fourier Transform preserves energy, i.e. the transform has the same exact energy as the signal does in the time domain. You can then find the energy of each frequency bin by multiplying its value with its complex conjugate.

Signal power represents how quickly it delivers energy. In the context of audio it correlates with how loud the sound is, though there is not a 1-to-1 correspondence.

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  • $\begingroup$ The last sentence is a gross over-simplification and in most cases simply wrong. $\endgroup$ – Hilmar Feb 18 '14 at 15:31
  • $\begingroup$ I was shooting for "correlates with loudness" not "directly proportional to loudness". I take it you interpreted it the second way. If so, my bad. $\endgroup$ – Jim Clay Feb 18 '14 at 18:37
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Any useful definition for power or energy in audio signals depends highly on context and application. While you can formally sum the squares of the samples and call it energy, the result isn't really useful for anything. It is NOT

  1. The energy delivered to the speakers
  2. The energy consumed by the amplifier
  3. Energy that the power supply needs to provide or that is drawn of the the wall outlet
  4. Acoustic energy radiated from the speaker
  5. Any measure on how loud it it.

All these are very different things and only loosely correlated. Without a specific goal of what you need "power" or "energy" for, it's difficult to properly define the term.

For example it's very easy to construct two signals, A and B, where A has twice the "energy" of B but is only half as loud as B.

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  • $\begingroup$ Numbers 1 and 4 are misleading. Yes, the energy measurement does have something to do with them, assuming the system is linear (which is a fairly good assumption for an audio system). $\endgroup$ – Jim Clay Feb 18 '14 at 18:41
  • $\begingroup$ Hence I'm calling then "loosely correlated". Sometimes they don't correlate at all. For example a class A/B amplifier consumes the most power when the signal delivered to the speaker is very small. $\endgroup$ – Hilmar Feb 19 '14 at 1:39

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