Abstract
Abstract
This paper describes the first algorithm for computing the inverse chirp z-transform (ICZT) in O(n log n) time. This matches the computational complexity of the chirp z-transform (CZT) algorithm that was discovered 50 years ago. Despite multiple previous attempts, an efficient ICZT algorithm remained elusive until now. Because the ICZT can be viewed as a generalization of the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, it has numerous practical applications in a wide variety of disciplines. This generalization enables exponentially growing or exponentially decaying frequency components, which cannot be done with the IFFT. The ICZT algorithm was derived using the properties of structured matrices and its numerical accuracy was evaluated using automated tests. A modification of the CZT algorithm, which improves its numerical stability for a subset of the parameter space, is also described and evaluated.
Publisher
Springer Science and Business Media LLC
Reference40 articles.
1. Bluestein, L. A linear filtering approach to the computation of discrete Fourier transform. In Proceedings of the Northeast Electronic Research and Engineering Meeting (NEREM), 218–219 (Boston, MA, 1968).
2. Rabiner, L. & Schafer, R. The use of an FFT algorithm for signal processing. In Proceedings of the Northeast Electronic Research and Engineering Meeting (NEREM), 224–225 (Boston, MA, 1968).
3. Rabiner, L., Schafer, R. & Rader, C. The chirp z-transform algorithm and its application. Bell Systems Technical Journal 48, 1249–1292 (1969).
4. Rabiner, L., Schafer, R. & Rader, C. The chirp z-transform algorithm. IEEE Transactions on Audio and Electroacoustics 17, 86–92 (1969).
5. Bluestein, L. A linear filtering approach to the computation of discrete Fourier transform. IEEE Transactions on Audio and Electroacoustics 18, 451–455 (1970).
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