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==== Generalization to arbitrary radices ====
The Bruun factorization, and thus the Bruun FFT algorithm, was generalized to handle arbitrary ''even'' composite lengths, i.e. dividing the polynomial degree by an arbitrary ''radix'' (factor), as follows. First, we define a set of polynomials φ<sub>''n'',α</sub>(''z'') for positive integers ''n'' and for α in <nowiki>[0,1)</nowiki> by:
:<math>\phi_{n, \alpha}(z) =
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