Mixed Square Waves Filtered vs. Sinewaves

Interesting premise. Therefore, in the future I will always shift my time reference to yield the 'simplest' FFT. thus, all sinusoidals are real. Ok, ok, a bit extreme. But interesting to always move the time reference of an 'arbitrary' time waveform, to yield the simplest FFT.

rms are again relative to the fundamental 0, 180, 0, 180 with the first term at -1i [I think] So that would be -90, +90, -90, +90 And, are all COMPLEX.

cycle square wave somehow automatically makes the frequency spectrum only REAL. Just not the case.

reference to yield the 'simplest' FFT. thus, all sinusoidals are real. Ok , ok, a bit extreme. But interesting to always move the time reference of an 'arbitrary' time waveform, to yield the simplest FFT.

I don't think you can do that for an arbitrary waveform. A 50% duty cycle s quare wave is a special case.

It's not just a 50% square wave that's special. It's all in the symmetry of the time-domain waveform. It its symmetry is odd w.r.t. to time zero, it will only have sine components. If its symmetry is even, it will only have cosines. If the time waveform has symmetry, it's possible to make all imaginary *or* all real components come out zero.

If it's not symmetric, it will have both sines and cosines. Whether you express this as two series of real numbers or a single series of complex ones is mostly a matter of taste.

Jeroen --A real number is just a complex number with a null imaginary part-- Belleman

Not a premise at all. You're always welcome to shift phase but the entire waveform has to shift. For an arbitrary waveform, what makes something simpler here, makes life more difficult elsewhere. Nature's a bitch. Perfectly symmetrical waveforms are a special case.