Discovering the Type of Waveform from a Fourier Series | Homework Help

In summary, the conversation discusses the use of Fourier series to create a sawtooth waveform. The input provided, 5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt), is not a valid input as it would result in continuously increasing voltage. The correct formula for the sawtooth waveform is 2*(-1)^{n+1}\over(\pi*n), where the peak amplitude is taken into account during the calculation of Bn and An.
  • #1
suv79
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0

Homework Statement



what type of waveform would this make ?

Homework Equations



V(t)=2/π(sin(ωt)+1/2sin(2ωt)+1/3sin(3ωt)+1/4sin(4ωt)+...)

5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt)...

The Attempt at a Solution

 

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  • #2
all that I have read about Fourier series, it uses odd number for 'n' to make an sawtooth waveform,

5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt)... this is not add together as it is increasing the voltage ?
 
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  • #3
Where did you come up with

suv79 said:
5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt)
 
  • #4
that is from the input, see the 2nd attached.
i don't understand what waveform the input will be making.
 
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  • #5
Those inputs I don't think are valid, cause you are right as they stand they'd keep adding.
Generally with Fourier series as the frequency of the component goes up the scalar goes down.
Take a look at http://en.wikipedia.org/wiki/Fourier_series
example 1 is actually the sawtooth waveform. You'll notice that is not 5 as you have in your example but rather [tex]2*(-1)^{n+1}\over(\pi*n)[/tex]
 
  • #6
the 5 is Peak amplitude.
 
  • #7
Well then it would be multiplied by 5. The peak amplitude is generally taken into account when you do the integral to calculate Bn & An
 

What is a Fourier series waveform?

A Fourier series waveform is a mathematical representation of a periodic waveform, such as a sound wave or an electrical signal. It is made up of a combination of sine and cosine functions with different amplitudes, frequencies, and phases.

What is the purpose of a Fourier series waveform?

The purpose of a Fourier series waveform is to break down a complex periodic waveform into simpler, easier to understand components. This allows us to analyze and manipulate the waveform in a more manageable way.

How is a Fourier series waveform calculated?

A Fourier series waveform is calculated by taking the Fourier transform of a periodic waveform. This involves decomposing the waveform into its individual frequency components using complex numbers and trigonometric functions.

What are the applications of Fourier series waveforms?

Fourier series waveforms have many applications in science and engineering, including analyzing and synthesizing audio signals, filtering noise from signals, and solving differential equations. They are also used in fields such as image processing, telecommunications, and signal processing.

How accurate is a Fourier series waveform?

A Fourier series waveform is an exact representation of a periodic waveform, meaning that it is completely accurate. However, its accuracy depends on the number of frequency components included in the series. The more components, the more accurate the representation will be.

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