Using Fourier to solve a problem.

[JoeBart]

I've been kicking this around for a few days. I know I'm overlooking something simple it has been a long time since I've had to do this. I'm trying to sketch the output in the time domain of a 1 kHz square wave passing through a communication channel whose bandwidth is 0 to 10 kHz.

I'm trying to apply: f(t) = Ao/2 + A1 cos ωt + A2 cos 2ωt + B2 sin 2ωt + ...

I'm just looking for direction here I believe I'm on the wrong track as I can't wrap my head around the equation without a known voltage.

 

[jfgobin]

Hey JoeBart,

If your link doesn't have any phase shift and an infinite attenuation at 10kHz, then you can truncate your Fourier series at the 9th term. However, in real life each harmonic will be slightly phased out, and the attenuation will not be infinite.

Here is what I have.

 

[JoeBart]

jfgobin,

Thank you!
This is what I expected to see. having been away for so long I'm having trouble solving the equation or putting the values in the correct places. I can visualize the output, but fail miserably at the math. I guess I'm looking for a little tutoring on the equation it self.

 

[vela]

Start by looking up the formulas for the Fourier coefficients.

 

[JoeBart]

vela,

This is where it all falls apart for me. The text I'm working from mentions A_n and B_n as being real-number coefficients, but never explains how to find them. I'm trying to teach myself how to take the information from the original problem and plug it into the Fourier series. After 22 years it's like learning to read hieroglyphs. I can see how the 3 filters mentioned in the problem affect the waveform, in my head, based on which harmonics are being attenuated. I would like to do this mathematically.

 

[berkeman]

vela,

This is where it all falls apart for me. The text I'm working from mentions A_n and B_n as being real-number coefficients, but never explains how to find them. I'm trying to teach myself how to take the information from the original problem and plug it into the Fourier series. After 22 years it's like learning to read hieroglyphs. I can see how the 3 filters mentioned in the problem affect the waveform, in my head, based on which harmonics are being attenuated. I would like to do this mathematically.

A good place to start to help refresh your memory is to do a Google Images search on Square Wave Spectrum. Then click on one of the simpler figures, and read the associated text at the website. You should be able to see how the coefficients of the harmonics roll off for an ideal square wave...

 

[vela]

This is where it all falls apart for me. The text I'm working from mentions A_n and B_n as being real-number coefficients, but never explains how to find them. I'm trying to teach myself how to take the information from the original problem and plug it into the Fourier series. After 22 years it's like learning to read hieroglyphs. I can see how the 3 filters mentioned in the problem affect the waveform, in my head, based on which harmonics are being attenuated. I would like to do this mathematically.

I'd check out another text then. Also, as Berkeman said, googling is a good thing to try. Fourier series is a popular subject, so you'll probably run across many good tutorials on it and worked examples, probably a much easier read than your textbook.

 

[JoeBart]

Thank you all for the guidance. I've already collected some great info from your suggestions.