Characterizing auditory neurons using the Wigner and Rihacek distributions: A comparison

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Abstract
Because of their dynamic properties, most sounds can best be characterized in the combined frequency-time (FT) domain. Powerful frequency-time characterizations are the Wigner distribution function (WDF) and the Rihacek energy density function (RDF). In the present paper several new concepts are introduced such as using the WDF to characterize the tuning of auditory neurons under wideband noise stimulation and a new method to quantify phase lock of auditory neurons to a wideband noise. No appreciable differences were found between the WDF and RDF in narrow-band signal representations. However, the differences between the WDF and RDF increase as the bandwidth of the signal increases. When signals are buried in uncorrelated background noise, the average FT function of these signals may be obtained through averaging the FT functions for each signal plus noise segment. The WDF takes at least a factor 2 more in time to compute than the RDF. The FT functions can be used to characterize (linear) filters by averaging FT functions of input-noise segments that precede threshold crossings of the filter’s output signal. Both the WDF and the RDF were used to characterize auditory neurons from the midbrain in anurans; the WDF always had a smaller bandwidth than the RDF. By comparing the spectrum of the reverse correlation function and the average spectrum of the noise segments preceding the spikes, a quantification of the amount of phase lock of the auditory neuron to the noise is obtained.