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 $$\sqrt2$$ of the amplitude. Alphax &tau;&epsilon;&chi; 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 &mdash; 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 &tau;&epsilon;&chi; 02:56, 30 Apr 2005 (UTC)