### Abstract

We formalise a functional implementation of the FFT algorithm over the complex numbers, and its inverse. Both are shown equivalent to the usual definitions of these operations through Vandermonde matrices. They are also shown to be inverse to each other, more precisely, that composition of the inverse and the transformation yield the identity up to a scalar.

### License

BSD License

### Topics

- Computer science/Algorithms/Mathematical

### Session FFT

- FFT

## Cite

×

FFT-AFP

    @article{FFT-AFP,
      author  = {Clemens Ballarin},
      title   = {Fast Fourier Transform},
      journal = {Archive of Formal Proofs},
      month   = {October},
      year    = {2005},
      note    = {\url{https://isa-afp.org/entries/FFT.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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