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Understanding Fourier Series: Finding f(t)
- Thread starter EugP
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- Fourier Fourier series Series
In summary: Alright, so I took your advice, but my results are still wrong. Here's what I did:a_v=\frac{1}{50}\int{40dt} from 0 to 50, and I got 40, but the answer is 0.
- #2
cristo
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Isn't f(t) the function for which you are attempting to find a Fourier series expansion?
- #3
EugP
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cristo said:
Yes, but in excersies that I've tried doing, I am not told f(t). I only get a graph usually.
- #4
cristo
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Can you not spot an equation for the graph? Why don't you post an example, and it'll be easier to help.EugP said:
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EugP
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cristo said:
Yes, here is one of the excersises. I need to find the Fourier series of that function:
- #6
Integral
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Use the graph to define your f(t). This called a piecewise function, it means you will need to break the integrals into pieces which correspond to the different parts of the function.
0 <= t < 50 f(t) = 40
50 <= t < 100 f(t) = 80
100 <= t < 150 f(t) = -40
150<= t <200 f(t) = -80
Now simply evaluate the integrals, using the different segments as that limits for each section.
0 <= t < 50 f(t) = 40
50 <= t < 100 f(t) = 80
100 <= t < 150 f(t) = -40
150<= t <200 f(t) = -80
Now simply evaluate the integrals, using the different segments as that limits for each section.
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EugP
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Integral said:
Alright, so I took your advice, but my results are still wrong. Here's what I did:
[tex]a_v=\frac{1}{T}\int{f(t)dt}[/tex]
[tex]a_v=\frac{1}{50}\int{40dt}[/tex]
from 0 to 50, and I got 40, but the answer is 0.
EDIT: The answer I got was correct, I just didn't finish. Thank you cristo and Integral for your help.
Last edited:
FAQ: Understanding Fourier Series: Finding f(t)
What is a Fourier series?
A Fourier series is a mathematical tool used to represent a periodic function as a sum of sines and cosines. It is named after the French mathematician Joseph Fourier, who first introduced the concept in the 19th century.
How is a Fourier series calculated?
A Fourier series is calculated using a formula that involves a combination of integrals and summations. Each term in the series represents a different frequency component of the original function.
Why is understanding Fourier series important?
Understanding Fourier series is important because they are used in a wide range of applications, including signal processing, image processing, and data compression. They allow us to break down complex functions into simpler, more manageable components.
What is the difference between a Fourier series and a Fourier transform?
A Fourier series is used for representing periodic functions, while a Fourier transform is used for non-periodic functions. Additionally, a Fourier series uses discrete frequencies, while a Fourier transform uses continuous frequencies.
What are some common applications of Fourier series?
Some common applications of Fourier series include audio and video compression, image and signal processing, and solving differential equations. They are also used in fields such as physics, engineering, and mathematics for analyzing and modeling periodic phenomena.