Fixed-point error analysis of radix-4 FFT

Radix-4 FFT requires less number of multiplications than radix-2 FFT of the same size, and for the same throughput, it requires less hardware. Hence, quite often, radix-4 structure is preferred to radix-2 structure. This paper evaluates the error performance of radix-4 FFT algorithms (the input quantization error and the coefficient inaccuracy is not considered). The analysis assumes fixed-point two's complement arithmetic, with rounding in the case of multiplication, and truncation in the case of scaling. The predicted results of output noise agree closely with the computer simulation results. The different schemes of scaling for preventing arithmetic overflow are compared from the noise-to-signal ratio point of view. In comparison with radix-2, the radix-4 FFT has got a marginally better error performance. © 1981.