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Numerical Accuracy of Fast Fourier Transforms with CORDIC Arithmetic

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Abstract

The vector rotation operation in the butterfly of a Fast Fourier Transform (FFT) can be calculated by a complex multiplier as well as a CORDIC (COordinate Rotation DIgital Computer). For these vector rotation blocks, expressions for the maximum numerical error are derived. It is shown that the error introduced by the CORDIC can be reduced by increasing the size of the input vector of the CORDIC and decreasing the size of the output vector by the same amount. This input vector scaling makes the reduction possible of the number of bits in the data path of the CORDIC. The impact on the Signal to Noise Ratio (SNR) of the FFT is evaluated when a CORDIC is applied in the FFT butterfly.

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Authors and Affiliations

  1. Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA, Eindhoven, The Netherlands

    M. Bekooij & J. Huisken

  2. Department of Electrical Engineering, Eindhoven University of Technology, The Netherlands

    K. Nowak

Authors
  1. M. Bekooij
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  2. J. Huisken
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  3. K. Nowak
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Bekooij, M., Huisken, J. & Nowak, K. Numerical Accuracy of Fast Fourier Transforms with CORDIC Arithmetic. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 25, 187–193 (2000). https://doi.org/10.1023/A:1008179225059

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  • DOI: https://doi.org/10.1023/A:1008179225059

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