User talk:Alphax/20050420-02

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 ${\sqrt {2}}$ of the amplitude. Alphax ^τεχ 08:40, 20 Apr 2005 (UTC)

Well, two things first: the RMS value of a sine wave is ${\frac {1}{\sqrt {2}}}$ 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 $f(x+T)=f(x)$): ${\frac {1}{\sqrt {3}}}$ times the amplitude
• triangle ($f(x)=T/4-\left|x\right|$ on [-T/2,T/2] and $f(x+T)=f(x)$): also ${\frac {1}{\sqrt {3}}}$
• square ($f(x)=\operatorname {sgn} \ x$ on [-T/2,T/2] and $f(x+T)=f(x)$): 1 (since its value is always $\pm 1$ 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)