Fourier Series
https://en.wikipedia.org/wiki/Pulse_wave
how to derive series waveforms
http://www.intmath.com/blog/mathematics/math-of-ecgs-fourier-series-4281
more detail on pg 324 of this pdf
http://www.wellesleycambridge.com/websections/cse41.pdf
harmonic content of PWM
https://en.wikipedia.org/wiki/Pulse-width_modulation
double-edge vs. leading/trailing edge PWM harmonic content
from http://www.springer.com/cda/content/document/cda_downloaddocument/9781447128847-c2.pdf?SGWID=0-0-45-1326538-p174291486
... the performance of the three bipolar PWM methods can be compared on the basis of their spectral
models (2.11), (2.13) and (2.15). To that end, note first that the carrier harmonics
and their sideband harmonics produced by trailing-edge bipolar PWM are equal
in amplitude to the corresponding harmonics in leading-edge modulation. Hence
these two methods have the same performance as far as harmonics are concerned.
To compare them with double-edge bipolar modulation, the amplitudes of the first
three carrier harmonics (m = 1, 2, 3) and their sideband components are tabulated
in Table 2.1 for n = ±1,±2,±3. The comparison shows that double-edge modulation
produces far fewer harmonics. ... In other words, double-edge modulation eliminates
all even-order sideband harmonics of even-order carrier harmonics, as well
as odd-order sideband harmonics of odd-order carrier harmonics. The reduced harmonic
content is a significant advantage of double-edge modulation and makes the
method more attractive for AC–DC and DC–AC converter application.
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