Understanding Complete Function Expansion: A Confusing Concept

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SUMMARY

The discussion centers on the concept of complete function expansion in the context of Fourier series, specifically addressing the confusion surrounding the coefficients a_n and b_n. It clarifies that while cosine and sine Fourier series use these coefficients for expansion, complete function expansion does not simply double the function when applied. The user ultimately resolves their confusion but highlights the complexity of understanding complete function expansion.

PREREQUISITES
  • Fourier series fundamentals
  • Understanding of sine and cosine functions
  • Knowledge of function expansion techniques
  • Basic mathematical analysis concepts
NEXT STEPS
  • Study the derivation of Fourier series coefficients
  • Explore the differences between sine, cosine, and complete Fourier expansions
  • Learn about convergence and divergence in Fourier series
  • Investigate applications of Fourier series in signal processing
USEFUL FOR

Mathematicians, physics students, and engineers interested in signal processing and function analysis will benefit from this discussion on complete function expansion.

flufypancakes
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i thought i understand it but i guess i don't...


you can expand a function in cosine f.s., sine f.s. and complete f.s. on some [0..L]. i thought that the coefficients a_n and b_n for complete expansion would come from sines and cosines respectively, but i guess that wouldn't make sense, since then your function will just double when expanded with complete f.s.

can someone explain this point to me please.
 
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already got it, never mind.

you guys suck...
 

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