FFT Performance in the Presence of Noise

Contamination of signals by noise degrades the performance of fast Fourier transform (FFT) analysis of biological systems. Thus, we have developed simulation techniques to investigate the effects of noise on FFT computations. Continuous and discrete representations of forcing-noise and response-noise signals are derived. The FFT is used to estimate magnitude and phase of noisy digital signals constructed using the discrete representations. The estimates are then compared to the estimates obtained from the noise-free digital signals. The following factors are shown to have an important influence on estimation accuracy: the inclusion of noninteger as well as integer harmonic noise, the signal series length, the relative noise-to-forcing and response signal magnitude ratios, and the degree of noise signal cross correlation between the forcing and response signals. We demonstrate that the FFT estimation accuracy of magnitude and phase is similar for integer and noninteger noise harmonics, it varies directly with signal series length, and inversely with the noise-to-forcing and response signal magnitude ratios.