Compound interest

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Revision as of 01:47, 16 January 2014 by en>Mark Arsten (Reverted edits by 76.28.21.126 (talk) to last revision by Mark Arsten (HG))
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In mathematics the finite Fourier transform may refer to either

or

or

  • a transform based on a Fourier-transform-like integral applied to a function x(t), but with integration only on a finite interval, usually taken to be the interval [0,T].[3] Equivalently, it is the Fourier transform of a function x(t) multiplied by a rectangular window function. That is, the finite Fourier transform X(ω) of a function x(t) on the finite interval [0,T] is given by:
X(ω)=12π0Tx(t)eiωtdt

References

  1. J. Cooley, P. Lewis, and P. Welch, "The finite Fourier transform," IEEE Trans. Audio Electroacoustics 17 (2), 77-85 (1969).
  2. George Bachman, Lawrence Narici, and Edward Beckenstein, Fourier and Wavelet Analysis (Springer, 2004), p. 264.
  3. M. Eugene, "High accuracy evaluation of the finite Fourier transform using sampled data," NASA technical report TME110340 (1997).

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