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The chirp z-transform algorithm

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3 Author(s)
L. Rabiner ; Bell Telephone Laboratories, Inc. Murray Hill, N.J. ; R. Schafer ; C. Rader

A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed. This algorithm has been named the chirp z -transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z -transform at M points in the z -plane which lie on circular or spiral contours beginning at any arbitrary point in the z -plane. The angular spacing of the points is an arbitrary constant, and M and N are arbitrary integers. The algorithm is based on the fact that the values of the z -transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N+M) \log _{2}(N+M) as opposed to being proportional to N . M for direct evaluation of the z -transform at M points.

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IEEE Transactions on Audio and Electroacoustics  (Volume:17 ,  Issue: 2 )