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.
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References
Marmor MF, Zrenner E. Standard for clinical electroretinography (1999 update). Doc Ophthalmol 1999; 97: 143–156.
Marmor M, Holder G, Porciatti V, Trick G, Zrenner E. Guidelines for basic pattern electroretinography. Recommendations by the International Society for Clinical Electrophysiology of Vision. Doc Ophthalmol 1996; 19: 291–8.
Simon F. The phase of PVEP in Maxwellian view: Influence of contrast, spatial and temporal frequency. Vision Res 1992; 32: 591–9.
Bach M, Meigen T, Strasburger H. Raster-scan cathode ray tubes for vision research – limits of resolution in space, time and intensity, and some solutions. Spatial Vision 1997; 10: 403–14.
Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes. The art of scientific computing. Cambridge: Cambridge University Press, 1986: Pages.
Papoulis A. Probability, random variables, and stochastic processes. New York: McGraw-Hill, 1984: Pages.
Cooley, JW, Tukey J. An algorithm for the machine calculation of complex fourier series. Math Comput 1965; 19: 297–301.
O'Neill MA. Faster than fast Fourier. Byte 1988; 4: 293–300.
Winograd S. On Computing the Discrete Fourier Transform. Math Comput 1978; 141: 175–99.
Victor JD, Mast J. A new statistic for steady-state evoked potentials. Electroenceph Clin Neurophysiol 1991; 78: 378–88.
Sieving PA, Arnold EB, Jamison J, Liepa A, Coats C. Submicrovolt flicker electroretinogram: Cycle-by-cycle recording of multiple harmonics with statistical estimation of measurement uncertainty. Invest Ophthalmol Vis Sci 1998; 39: 1462–9.
Meigen T, Bach M. On the statistical significance of electrophysiological steady-state responses. Doc Ophthalmol 1999; 98: 207–232.
Strasburger H. The analysis of steady state evoked potentials revisited. Clin Vision Sci 1987; 1: 245–56.
Norcia AM, Tyler CW, Hamer RD, Wesemann W. Measurement of spatial contrast sensitivity with the swept contrast VEP. Vision Res 1989; 29: 627–37.
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Bach, M., Meigen, T. Do's and don'ts in Fourier analysis of steady-state potentials. Doc Ophthalmol 99, 69–82 (1999). https://doi.org/10.1023/A:1002648202420
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DOI: https://doi.org/10.1023/A:1002648202420