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# When Fourier series coeficient 1 is zero

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#### Highlander-SP

##### Member level 3
If I have a function that the coeficients a0=0; an=0; b1=0 and b2, b3, ..., bn ≠ 0
may I have to consider that the fundamental is b2?

what do u mean by b2 is fundamental. pls be precise with ur question

thnx

purna!

fourier series
f = a0 + ∑[an cos(n wo t) + bn sin(n wo t)]
a0 = average or dc value of the function
a1,b1 = coefficients of the fundamental harmonic (wo)
a2,b2 = coefficients of the second harmonic (2×wo)
.... etc

mas

No - in something like music, the fundimental is the frequency which all the other harmonics are integer multiples of.
If all the odd b coefficients were 0, and b2,b4... were not zero, the answer would be yes.

I think your fundimental is given by b1, even though its amplitude is zero.
(like a signal with a suppressed carrier - there is no carrier, but the remaining signal implies it)

In addition (music again) - distortion will cause intermods, and b1 will surface.

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