# complex waveforms

## I attached my attempt if someone can comment on it please.

• ### attached a hybrid function picture above

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#### minius

Joined Jan 10, 2015
5
Sketch the waveform defined below and explain how you would obtain its Fourier series:
f (wt) = 0 for 0≤wt ≤ pi/2
f (wt) = Vsin(wt) for pi/2≤wt ≤pi
f (wt) = 0 for pi≤wt ≤3pi/2
f (wt) = Vsin(wt) for 3pi/2≤wt ≤2pi
Develop the analysis as far as you are able.

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#### MrAl

Joined Jun 17, 2014
8,556
Hi,

Have you done any other Fourier series' ?
You do this the same way but only integrate over the period(s) that are non zero while still using the complete period as the total period.
This looks like a half wave rectified minus sine wave.

#### minius

Joined Jan 10, 2015
5
This is a new subject for me and I am trying to study and understand the concept. If you can give us a hint it would be appreciated. I believe I need to calculate a0, an, bn coefficients is that correct? I would appreciate any help you can provide.

#### WBahn

Joined Mar 31, 2012
26,398
Sketch the waveform defined below and explain how you would obtain its Fourier series:
f (wt) = 0 for 0≤wt ≤ pi/2
f (wt) = Vsin(wt) for pi/2≤wt ≤pi
f (wt) = 0 for pi≤wt ≤3pi/2
f (wt) = Vsin(wt) for 3pi/2≤wt ≤2pi
Develop the analysis as far as you are able.
What's Vsin(wt) at wt=pi/2?

What's Vsin(wt) at wt=3pi/2?

Do either of those agree with your sketch?

#### minius

Joined Jan 10, 2015
5
WBahn thank you for reply. I think they part of sinwave. for the second 3π/2×180º/π = 270º sin is -1 so should be going down on y axis?

#### WBahn

Joined Mar 31, 2012
26,398
WBahn thank you for reply. I think they part of sinwave. for the second 3π/2×180º/π = 270º sin is -1 so should be going down on y axis?
If the voltage is -V at that point in the waveform, then, yah, I think the sketch should reflect that. Don't you?

If necessary, evaluate the function had three or four points within each section and plot those to make sure that your sketch is consistent with the function it's representing. There's no need to guess at this.

#### minius

Joined Jan 10, 2015
5
thank you

#### MrAl

Joined Jun 17, 2014
8,556
Hi,

Yes your waveform drawing is not correct yet. It should look like a triac waveform turning on at two places in the cycle.
You are right that you need to calculate a0 and the an, and bn. Some may turn out to be zero.

#### minius

Joined Jan 10, 2015
5
thanks again MrAl I think I know the sketch and I have a0 = 0 in my calcs but an and bn that looks challenging to me.Any hints on that? this sin(wt) confuses me...

#### WBahn

Joined Mar 31, 2012
26,398
thanks again MrAl I think I know the sketch and I have a0 = 0 in my calcs but an and bn that looks challenging to me.Any hints on that? this sin(wt) confuses me...
Well, show your work so that we can see if you are even starting out correctly and, if you are, where you are going astray. We are not mind readers.