Discrimination of the spectral density of multitone complexes

Mathematical framework for place coding in the auditory system

In the auditory system, tonotopy is postulated to be the substrate for a place code, where sound frequency is encoded by the location of the neurons that fire during the stimulus. Though conceptually simple, the computations that allow for the representation of intensity and complex sounds are poorly understood. Here, a mathematical framework is developed in order to define clearly the conditions that support a place code. To accommodate both frequency and intensity information, the neural network is described as a space with elements that represent individual neurons and clusters of neurons. A mapping is then constructed from acoustic space to neural space so that frequency and intensity are encoded, respectively, by the location and size of the clusters. Algebraic operations -addition and multiplication- are derived to elucidate the rules for representing, assembling, and modulating multi-frequency sound in networks. The resulting outcomes of these operations are consistent with network simulations as well as with electrophysiological and psychophysical data. The analyses show how both frequency and intensity can be encoded with a purely place code, without the need for rate or temporal coding schemes. The algebraic operations are used to describe loudness summation and suggest a mechanism for the critical band. The mathematical approach complements experimental and computational approaches and provides a foundation for interpreting data and constructing models.

Exponential spectro-temporal modulation generation

Traditionally, real-time generation of spectro-temporally modulated noise has been performed on a linear amplitude scale, partially due to computational constraints. Experiments often require modulation that is sinusoidal on a logarithmic amplitude scale as a result of the many perceptual and physiological measures which scale linearly with exponential changes in the signal magnitude. A method is presented for computing exponential spectro-temporal modulation, showing that it can be expressed analytically as a sum over linearly offset sidebands with component amplitudes equal to the values of the modified Bessel function of the first kind. This approach greatly improves the efficiency and precision of stimulus generation over current methods, facilitating real-time generation for a broad range of carrier and envelope signals.