A fourier approximation of a square wave of amplitude X has to include frequencies with amplitude greater than X, so it doesn't strike me as paradoxical that the RMS would average out to the correct value... am I missing the puzzle? On Sun, Nov 12, 2017 at 5:04 PM, James Propp <jamespropp@gmail.com> wrote:
Keith,
The root mean square (RMS) of a sine wave is always the peak value
divided by the square root of 2. The same is true of the sums of multiple sine waves with different frequencies, phases, and amplitudes.
My skepticism kicks in at that step. For a sum of two sine waves, I might believe it, but not for the sum of arbitrarily many.
But every repeating waveform is equal to the sum of
sine waves with different frequencies, phases, and amplitudes. This
includes the square wave, i.e. a function which always equals +X or -X, and never takes any other value. But obviously the RMS of that square wave is simply X, not X divided by the square root of 2. Explain.
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