Question

Hi guys, I have been given a question to solve:

Determine the first four terms of the Fourier series for the waveform shown in the diagram.

I am then given a square wave with a peak of 5V to -0.5V and am given the points 3π/2 and 2π at the transitions from 5V to -0.5V and -0.5V to 5V.

I hope that makes sense as I can't paste the waveform in but I could really do with an idiots guide to doing this. Thanks

Answer 1

here is the waveforem

Answer 2

f(x) is an odd function so: an=a0=0 \[bn=1/\pi \int\limits_{0}^{2\pi}f(x)\sin(nx)dx=1/\pi \int\limits_{0}^{3\pi/2}5\sin(nx)dx+1/\pi \int\limits_{3\pi/2}^{2\pi}(-1/2)\sin(nx)dx\] After calculations:
bn=1/(2pi*n) when n is odd \[bn=-\frac{ 5 }{ n \pi }(-1)^{n/2}+\frac{ 1 }{ 2n \pi }(1-(-1)^{n/2}) when n is even\] Finally: \[S _{4}(x)=\sum_{n=1}^{4}bn*\sin(nx)=\frac{ 1 }{ 2\pi }\sin(x)+\frac{ 3 }{ \pi }\sin(2x)+\frac{ 1 }{ 6\pi }\sin(3x)-\frac{ 5 }{ 4\pi }\sin(4x)\]
Haven't done this in a long time so you might wanna check !

Answer 3

great thankyou so much

Answer 4

You're welcome !