Correcting for the Alias Effect When Measuring the Power Spectrum Using a Fast Fourier Transform

  title={Correcting for the Alias Effect When Measuring the Power Spectrum Using a Fast Fourier Transform},
  author={Yuan Jing},
  journal={The Astrophysical Journal},
  • Y. Jing
  • Published 2004
  • Physics
  • The Astrophysical Journal
Because of mass assignment onto grid points in the measurement of the power spectrum using a fast Fourier transform (FFT), the raw power spectrum [|delta(f)(k)|(2)] estimated with the FFT is not the same as the true power spectrum P( k). In this paper we derive a formula that relates h|delta(f)(k)|(2)] to P( k). For a sample of N discrete objects, the formula reads [\delta(f) ( k)\(2)] = Sigma(n) [\W( k + 2k(N)n)\(2) P( k + 2(k)Nn) +1\N\W(k+2k(N)n)\(2)], where W(k) is the Fourier transform of… Expand

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