Dual Chirp-Z Transform

J. M. Speiser; H. J. Whitehouse

doi:10.1117/12.957316

21 September 1979 Dual Chirp-Z Transform

J. M. Speiser, H. J. Whitehouse

Proceedings Volume 0180, Real-Time Signal Processing II; (1979) https://doi.org/10.1117/12.957316
Event: Technical Symposium East, 1979, Washington, D.C., United States

Abstract

Performing the Discrete Fourier Transform via convolution using a transversal filter is attractive since it potentially provides a high speed, low power, low cost implementation. Previous papers have discussed two such algorithms and their associated device architectures: the Chirp-Z transform and the Prime transform. The Chirp-Z transform (CZT) performs the DFT as the succession of a point-by-point multiplication, a convolution, and a second point-by-point multiplication. The Prime transform is similar except that the point-by-point multiplications are replaced by permutations. To date, the accuracy of CZT implementations has been limited by multiplier errors, and the accuracy of Prime Transform implementations has been limited by permuter errors. Errors in the point-by-point postmultiplication or permutation are particularly troublesome, since no subsequent convolution is performed to average out the effect of such errors. The Dual Chirp-Z transform (Dual CZT) algorithm performs a discrete Fourier transform via successive convolution, point-by-point multiplication, and a second convolution. When the transform block size is even, the required reference functions for the convolutions and point-by-point multiplications become discrete chirps. Because the final operation is a convolution, the Dual CZT appears potentially attractive for the more accurate implementation of the discrete Fourier transform via transversal filters. If the block length is even, then the same transversal filters which would be used for the ordinary CZT may be used for the Dual CZT. Only the final summing device in the second complex filter needs to be modified to provide an equivalent change of the tap weights by a factor of (1 + i).

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J. M. Speiser and H. J. Whitehouse "Dual Chirp-Z Transform", Proc. SPIE 0180, Real-Time Signal Processing II, (21 September 1979); https://doi.org/10.1117/12.957316

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KEYWORDS

Convolution

Filtering (signal processing)

Digital filtering

Fourier transforms

Electronic filtering

Quantization

Signal processing

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