Numerical accuracy of fast Fourier transforms with CORDIC arithmetic

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 (COordi nate Rotation DIgital Computer). For these vector rotation blocks, expressi ons 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 inpu t 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 F FT butterfly.