Coefficient ck of the fourier series

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SUMMARY

The discussion focuses on calculating the coefficients \( c_k \) for the Fourier series of the piecewise function defined as \( f(t) = 0 \) for \( -\pi \leq t < 0 \) and \( f(t) = t \) for \( 0 \leq t < \pi \). Participants noted that different coefficients arise for even and odd indices, specifically \( c_{2k} = f(2k) \) and \( c_{2k+1} = g(2k+1) \). The conversation emphasizes the need for clarity in representing these coefficients within the Fourier series framework.

PREREQUISITES
  • Understanding of Fourier series and their applications
  • Familiarity with complex and real functions
  • Knowledge of piecewise functions
  • Basic calculus for integration and summation
NEXT STEPS
  • Study the derivation of Fourier coefficients for piecewise functions
  • Learn about the convergence properties of Fourier series
  • Explore the differences between complex and real Fourier series
  • Investigate the implications of even and odd functions in Fourier analysis
USEFUL FOR

Mathematics students, engineers, and anyone involved in signal processing or harmonic analysis will benefit from this discussion on Fourier series coefficients.

Luongo
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1. find the complex Fourier series and the real Fourier series
f(t) = 0 , -pi <= t < 0, f(t)= t, 0<=t< pi



Homework Equations





3. to find the coefficient ck i got 2 different answers one is if the index k is even and another if the index is odd, how am i supposed to represent this in the Fourier series?
 
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Hi Luongo! :smile:

(have a pi: π :wink:)

c2k = f(2k)

c2k+1 = g(2k+1) :wink:​
 

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