There are some elemental technical errors in the video. So elemental that someone of
@amirm's stature should not be making any of them - particularly in a publication. Playing around with the AP is nice but seemingly not knowing what one in talking about fails to serve the purpose of education and calls into question not only your competence but also your sincerity,
@amirm.
Square waves having infinite energy (3:23, 8:48) (how is that even relevant?) would require that there be some other corresponding infinite energy somewhere in the universe to ensure energy conservation, which is binding at the time scale used here. That would be quite amazing and constitute its own new theory contrary to the current predominant theories.
While the sum of the coefficients in the Fourier transform indeed approaches infinity as the number of harmonics does, the sum itself does not at any point of the cycle. This is due to the periods of the harmonics being different from that of the square.
Further, since power is the time rate of energy, i.e. for constant energy, power is energy divided by time, infinite energy would require either infinite power or zero time. The latter is certainly not the case, while the former is not either since the power of an electrical signal is the product of voltage and current - either of which are finite due to charge conservation and there being a finite number of charged particles in the universe (unless new theory as above). Also, infinite power out of an outlet under normal operation should not pass any sanity check.
Also, the slope here is change in voltage relative to change in time. For a vertical curve (4:50), the slope is not zero but infinite. The slope of a sine wave at a zero crossing is proportional to frequency. Thus the greater the slope, the greater the frequency. Zero slope corresponds to a constant, i.e. a horizontal curve.
