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A linear filtering approach to the computation of discrete Fourier transform

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1 Author(s)
Bluestein, Leo I. ; General Telephone and Electronics Laboratories, Inc., Waltham, Mass.

It is shown in this paper that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process. We show further that the chirp filter should not be realized as a transversal filter in a wide range of cases; use instead of the conventional FFT permits the computation of the DFT in a time proportional to N \log _{2} N for any N, N being the number of points in the array that is transformed. Another proposed implementation of the chirp filter requires N to be a perfect square. The number of operations required for this algorithm is proportional to N^{3/2} .

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Audio and Electroacoustics, IEEE Transactions on  (Volume:18 ,  Issue: 4 )