1969/05/06 by Lawrence R. Rabiner, Ronald W. Schafer, Charles M. Rader · 2 citations
Computer Science · #Blind Source Separation Techniques #Digital Filter Design and Implementation #Image and Signal Denoising Methods
paper · doi:10.1002/j.1538-7305.1969.tb04268.x
crossref issued 1969/05/06 · crossref published 1969/05/06 · crossref published-print 1969/05/06 · openalex publication_date 1969/05/06 · crossref published-online 2013/07/29 · crossref created 2013/07/29 · crossref deposited 2022/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31 · crossref indexed 2026/07/31
We discuss a computational algorithm for numerically evaluating the z-transform of a sequence of N samples. This algorithm has been named the chirp z-transform algorithm. Using this 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; 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) log2(N + M) as opposed to being proportional to N · M for direct evaluation of the z-transform at M points. Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fourier transform program.