On the fixed-point accuracy analysis of FFT algorithms

Abstract—In this paper, we investigate the effect of fixed-point arithmetics with limited precision for different fast Fourier trans-form (FFT) algorithms. A matrix representation of error propaga-tion model is proposed to analyze the rounding effect. An analytic expression of overall quantization loss due to the arithmetic quanti-zation errors is derived to compare the performance with decima-tion-in-time (DIT) and decimation-in-frequency (DIF) configura-tions. From the simulation results, the radix-2 DIT FFT algorithm has better accuracy in term of signal-to-quantization-noise ratio (SQNR). Based on the results, a simple criterion of wordlength op-timization is proposed to yield comparable accuracy with fewer bit budget