Observations on Fourier Sum

• Smooth functions f(x) require few coefficients bn

• Sharp functions (square wave) require more coefficients

• Large-n coefficients describe high-frequency behavior of f(x)

  • large n = short wavelength

• Small-n coefficients describe low-frequency behavior

  • small n = long wavelength
  • e.g., n = 0 coefficient is simple average of f(x)

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