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noohac's avatar

How do you find the phase shift in a Fourier Series?

Asked by noohac (101 points ) May 2nd, 2010

Specifically in electricity, I am unsure how to find the phase shift of a Fourier Series that represents a current. The period is 20ms. The particular problem I have a Co =3.2mA and a Cn magnitude of 8/(n*pi)sin(4*pi/5). When I want to put in in the Cn complete form I get to 3.2 + (sigma) 8/(n*pi)sin(4*pi/5)cos(n(2*pi)/(20E-3)t + ????) = i(t) Where the ???? is the phase shift I am unsure of. I have tabled the magnitudes of n= 1 to 6 and I realize there is a magnitude of 0 at 5. I think the phase can be in a closed form because the magnitude is purely real but have no idea where to go from there.

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3 Answers

roundsquare's avatar

Oh man… this makes me so sad. I’ve forgotten everything about this.

However, I think you can take your Fourier transform and look at the peak and see how far that is from t = 0. But don’t quote me on it.

Side note: I wouldn’t mind more science questions here. Always a good way to learn.

lilikoi's avatar

I have forgotten a lot all of this, too! :(

I think maybe you can combine the sin and cos terms into a single function somehow (you know like sin 2x =2 sin x cos x – or something like that, not sure what it was exactly, but there were several different relationships like this) then look at what x is, and if it takes the form of something like this, then the phi in the equation is your phase shift by definition.

@roundsquare agree – questions like this are good refreshers for me :)

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