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This paper presents a theory by which idealized models of auditory receptivefields can be derived in a principled axiomatic manner, from a set ofstructural properties to enable invariance of receptive field responses undernatural sound transformations and ensure internal consistency betweenspectro-temporal receptive fields at different temporal and spectral scales.  For defining a time-frequency transformation of a purely temporal soundsignal, it is shown that the framework allows for a new way of deriving theGabor and Gammatone filters as well as a novel family of generalized Gammatonefilters, with additional degrees of freedom to obtain different trade-offsbetween the spectral selectivity and the temporal delay of time-causal temporalwindow functions.  When applied to the definition of a second-layer of receptive fields from aspectrogram, it is shown that the framework leads to two canonical families ofspectro-temporal receptive fields, in terms of spectro-temporal derivatives ofeither spectro-temporal Gaussian kernels for non-causal time or the combinationof a time-causal generalized Gammatone filter over the temporal domain and aGaussian filter over the logspectral domain. For each filter family, thespectro-temporal receptive fields can be either separable over thetime-frequency domain or be adapted to local glissando transformations thatrepresent variations in logarithmic frequencies over time. Within each domainof either non-causal or time-causal time, these receptive field families arederived by uniqueness from the assumptions.  It is demonstrated how the presented framework allows for computation ofbasic auditory features for audio processing and that it leads to predictionsabout auditory receptive fields with good qualitative similarity to biologicalreceptive fields measured in the inferior colliculus (ICC) and primary auditorycortex (A1) of mammals.

Idealized computational models for auditory receptive fields