User talk:Alphax/20050420-02

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[edit] Root mean square functions

What are the RMS functions for various waveforms as a function of the amplitudes? Eg. RMS of a sine wave is \sqrt2 of the amplitude. Alphax τεχ 08:40, 20 Apr 2005 (UTC)

Well, two things first: the RMS value of a sine wave is \frac1\sqrt2 of the amplitude. Also note that "the" RMS value of a waveform depends on where it's centered — for the following I've assumed that the mean value of the wave is 0 (as is usually the case in this context). Using the continuous function formula at RMS, I get
  • sawtooth (f(x) = x on [-T/2,T/2] and f(x + T) = f(x)): \frac1\sqrt3 times the amplitude
  • triangle (f(x)=T/4-\left|x\right| on [-T/2,T/2] and f(x + T) = f(x)): also \frac1\sqrt3
  • square (f(x)=\operatorname{sgn}\ x on [-T/2,T/2] and f(x + T) = f(x)): 1 (since its value is always \pm1 times the amplitude
Those are the standard waveforms I know about -- if you want more you'll have to specify them! --Tardis 02:09, 30 Apr 2005 (UTC)
Thankyou! I knew square, and I figured sawtooth and triangle would be the same. (How much of this can be added to the RMS article?) Many thanks, Alphax τεχ 02:56, 30 Apr 2005 (UTC)
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