On the Fixed-Point Accuracy Analysis of FFT Algorithms
In this paper, we investigate the effect of fixed-point arithmetics with limited precision for different fast Fourier transform (FFT) algorithms. A matrix representation of error propagation model is proposed to analyze the rounding effect. An analytic expression of overall quantization loss due to the arithmetic quantization errors is derived to compare the performance with decimation-in-time (DIT) and decimation-in-frequency (DIF) configurations. 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 optimization is proposed to yield comparable accuracy with fewer bit budget.