Accurate performance analysis of a fixed point FFT

Fast Fourier Transform (FFT) algorithm is widely used in today's digital signal processing applications. In practice, fixed point arithmetic is used for hardware implementations. The finite bits representation of signals introduces quantization error and thereby limits its accuracy. In this paper, we present a technique to estimate accurately the impact of fixed point arithmetic on FFT performance. We evaluate the fixed point accuracy by measuring Signal-to-Quantization Noise Ratio (SQNR) of 2ⁿ (=N) Radix-2 FFT implementation. This SQNR analysis is used to determine fixed point precisions of the FFT implementation that provides a good trade-off between the required hardware resources and final FFT output signal integrity. In the end, we will present the simulation results to illustrate the accuracy of the theoretical analysis.