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Topic: Fourier Synthesis of a Square Wave (Read 3240 times) previous topic - next topic
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Fourier Synthesis of a Square Wave

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.