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A functional representation is proposed for complex valued (amplitude and phase) head-related transfer functions (HRTFs), including both frequency and spatial dependence. The frequency variation is spanned by a set of eigentransfer functions (EFs) that are generated using the Karhunen-Loève expansion. Any HRTF is represented as a weighted combination of the EFs where the weights are functions of the HRTFs spatial location and are termed spatial characteristic functions (SCFs). Samples of the SCFs are obtained by projecting the measured HRTFs onto the EFs. A regularization framework is employed to obtain a functional representation for the SCFs by fitting each set of SCF samples with a two-dimensional spline. Acoustic validation of the model's fidelity and predictive capability is provided using 2188 measured HRTFs from a KEMAR manikin and 1816 measured HRTFs from an anesthetized live cat. Errors between measured and modeled HRTFs are generally less than one percent. Larger errors occur in the contralateral regions for KEMAR and lower back regions for the cat as a consequence of the relatively small HRTF amplitudes resulting from head shadowing. Methods for reducing these errors are discussed.

A spatial feature extraction and regularization model for the head-related transfer function