# HydrogenAudio

## Hydrogenaudio Forum => Scientific Discussion => Topic started by: dosdan on 2003-10-08 23:28:56

Title: Fourier Synthesis of a Square Wave
Post by: dosdan on 2003-10-08 23:28:56
I'm trying to demonstrate Fourier synthesis of a square wave. I've done this before but this time it's not quite going the way I expect it too.  In the formulas below I've got a multiplications and divisions that could be simplified but I've left them as is to show the sequence a little more clearly. In a1:a37 if got a fill sequence of 0:360 in steps. I'm comparing a small number of harmonics (4) with a larger number (20):

=SIN(\$A1*PI()/180)+SIN(3*\$A1*PI()/180)/3+SIN(5*\$A1*PI()/180)/5+SIN(7*\$A1*PI()/180)/7+SIN(9*\$A1*PI()/180)/9

vs.

=SIN(\$A1*PI()/180)+SIN(3*\$A1*PI()/180)/3+SIN(5*\$A1*PI()/180)/5+SIN(7*\$A1*PI()/180)/7+SIN(9*\$A1*PI()/180)/9+SIN(11*\$A1*PI()/180)/11+SIN(13*\$A1*PI()/180)/13+SIN(15*\$A1*PI()/180)/15+SIN(17*\$A1*PI()/180)/17+SIN(19*\$A1*PI()/180)/19+SIN(21*\$A1*PI()/180)/21+SIN(23*\$A1*PI()/180)/23+SIN(25*\$A1*PI()/180)/25+SIN(27*\$A1*PI()/180)/27+SIN(29*\$A1*PI()/180)/29+SIN(31*\$A1*PI()/180)/31+SIN(33*\$A1*PI()/180)/33+SIN(35*\$A1*PI()/180)/35+SIN(37*\$A1*PI()/180)/37+SIN(39*\$A1*PI()/180)/39

As expected, the top of the waveform is flattening off nicely but I think the last time I did this the change in risetime/falltime was much more pronounced with more harmonics. Shouldn't the dV/dt increase with more harmonics and become more abrupt?.  So far, the rise and fall parts are too much the same.