Obtaining meaningful results from Fourier deconvolution of reaction time data

The technique of Fourier deconvolution is a powerful tool for testing distributional predictions of stage models of reaction time. However, direct application of Fourier theory to reaction time data has sometimes produced disappointing results. This article reviews Fourier transform theory as it applies to the problem of deconvolving a component of the reaction time distribution. Problems encountered in deconvolution are shown to be due to the presence of noise in the Fourier transforms of the sampled distributions, which is amplified by the operation of deconvolution. A variety of filtering techniques for the removal of noise are discussed, including window functions, adaptive kernel smoothing, and optimal Wiener filtering. The best results were obtained using a window function whose pass band was determined empirically from the power spectrum of the deconvolved distribution. These findings are discussed in relation to other, nontrigonometric approaches to the problem of deconvolution.