Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform

@article{Morgenstern1973NoteOA,
  title={Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform},
  author={Jacques Morgenstern},
  journal={J. ACM},
  year={1973},
  volume={20},
  pages={305-306}
}
A lower bound for the number of additions necessary to compute a family of linear functions by a linear algorithm is given when an upper bound <italic>c</italic> can be assigned to the modulus of the complex numbers involved in the computation. In the case of the fast Fourier transform, the lower bound is (<italic>n</italic>/2) log<subscrpt>2</subscrpt><italic>n</italic> when <italic>c</italic> = 1. 
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