The DFT is presented as the diagonalization of a circulant matrix, the FFT as a recursive matrix factorization, and the same scheme is generalized to finite abelian groups via G-circulants.
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Discrete and Fast Fourier Transform Made Clear
The DFT is presented as the diagonalization of a circulant matrix, the FFT as a recursive matrix factorization, and the same scheme is generalized to finite abelian groups via G-circulants.