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The amplitudes of FM sidebands are given by

  • A.The Fourier coefficients of a square wave
  • B.Legendre polynomials
  • C.Bessel functions of the first kind
  • D.Powers of the modulation index

Answer: C

Each sideband amplitude is \( J_n(\beta) \), a Bessel function of the first kind, evaluated at the modulation index, which is why FM spectra are tabulated rather than computed by hand. Simple powers of the index describe only the narrowband approximation. Square-wave coefficients arise from a different problem entirely. And Legendre polynomials belong to spherical geometry. The Bessel behaviour also explains the carrier nulls, which occur at particular indices and are used to calibrate deviation.

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