Finding a Fourier Series: What to Do and How?

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SUMMARY

The discussion focuses on finding a Fourier series for the function f(t) = a cos(kt) + b cos(kt) using Fourier coefficients. The method involves applying the formula ck = (1/2π) ∫ f(t)e^(-ikt) dt to derive the coefficients. Participants emphasize the necessity of converting the function into exponential form, leading to four different exponential terms and subsequent integrations. The final recommendation is to express the complex series in terms of sine and cosine by utilizing the identity e^(iθ) = cos(θ) + i sin(θ).

PREREQUISITES
  • Understanding of Fourier series and coefficients
  • Familiarity with complex exponential functions
  • Knowledge of integration techniques
  • Ability to manipulate trigonometric identities
NEXT STEPS
  • Study the derivation of Fourier coefficients using ck = (1/2π) ∫ f(t)e^(-ikt) dt
  • Learn how to convert trigonometric functions to exponential form
  • Explore the process of transforming complex series into sine-cosine series
  • Investigate practical applications of Fourier series in signal processing
USEFUL FOR

Mathematicians, engineering students, and anyone involved in signal analysis or harmonic analysis will benefit from this discussion.

Luongo
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1. We are supposed to find a Fourier series knowing only f(t)= acos(kt)+bcos(kt)
and some values of Fourier coefficients...

please see #2 on this link http://www.math.ubc.ca/~oyilmaz/courses/m267/hmk3.pdf
2. I am using ck=1/2pi \intf(t)e<sup>-ikt</sup>dt
3. are we supposed to convert f(t) into expnential form? i got 4 different expos thus 4 integrations, i have no idea which method i should solve it...
 
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You only have 5 nonzero coefficients. Write out the 5 term complex series and then change it to a sine-cosine series using eiθ = cos(θ) + i sin(θ) and collecting terms.
 

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