- #1
Understanding Fourier Series: Finding f(t)
- Thread starter EugP
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- Fourier Fourier series Series
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Discussion Overview
The discussion revolves around understanding how to determine the function f(t) when working with Fourier series, particularly in the context of exercises where only a graph is provided. Participants explore the process of defining f(t) from graphical representations and the subsequent steps to evaluate the Fourier series.
Discussion Character
- Exploratory
- Technical explanation
- Homework-related
Main Points Raised
- One participant expresses confusion about identifying f(t) when only given a graph, seeking clarification on how to proceed.
- Another participant suggests that f(t) is the function for which a Fourier series expansion is being sought.
- A participant emphasizes the need to derive an equation from the graph and encourages posting an example for better assistance.
- A later reply provides a piecewise definition of f(t) based on the graph, outlining specific intervals and corresponding function values.
- One participant shares their attempt at calculating the Fourier coefficients but initially believes their result is incorrect, later clarifying that they simply did not complete the calculation.
Areas of Agreement / Disagreement
Participants generally agree on the need to define f(t) from the graph, but there is no consensus on the specific methods or interpretations of the results, as one participant initially misinterprets their calculations.
Contextual Notes
The discussion highlights the challenge of translating graphical information into mathematical functions, with specific attention to piecewise functions and the evaluation of integrals. There are unresolved aspects regarding the completeness of calculations and the interpretation of results.
- #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:
- #5
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.
- #7
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:
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