##  [Fast Fourier Transform](/fast-fourier-transform) 

  ##  [Fast Fourier Transform](https://mathlogic.quantumdictionary.io/fast-fourier-transform-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algorithmic family that computes the discrete Fourier transform (DFT) of a sequence efficiently by exploiting symmetries, periodicities, and recursive factorization of the DFT matrix to reduce arithmetic complexity from O(N^2) to O(N log N) in common cases.