Analysis of Quantization Noise in FFT Algorithms for Real-Valued Input Signals
Monther Alrwashdeh, Zsolt Kollár · 2022
In this paper, we investigate the effect of quantization noise in radix-2 Decimation in Time Fast Fourier Transform (DIT-FFT) algorithms for the special case where the Discrete Fourier Transform (DFT) of two real-valued input signals are required to be calculated in parallel. We consider fixed-point and floating-point quantization independently as well. Three algorithms for calculating the DFT of two real-valued input signals will be analyzed: applying two separate FFTs, applying a single FFT with additional signal processing steps, and two half sized FFTs with additional signal processing steps. The three algorithms are investigated through simulations using fixed-point and single precision floating-point quantization. The results are compared with that of the double precision floating-point implementation. Furthermore, the Quantization Noise Power (QNP) of these algorithms are expressed analytically as well. The results of the QNP are expressed in function of the length of the FFT and the number of bits used for the calculations.