Do's and don'ts in Fourier analysis of steady-state potentials

Abstract

Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically:

• In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so `windowing' and calculation of the `periodogram' are not necessary.

• It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator.

• The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods.

• The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number `spills' noise into the response frequency.

• There is no need to feel tied to a power-of-two number of data points as required by standard FFT, `resampling' is an easy and efficient alternative.

• Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise.

These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.