Date of Award


Document Type


Degree Name




First Advisor

Mohammad A. Matin, Ph.D.

Second Advisor

Daniel J. Tollin, Ph.D.


Directional transfer function, First notch, Head related transfer function, Interpolation, Pole zero models, Virtual auditory display


Directional transfer functions (DTFs), the directional components of the Head Related Transfer Functions (HRTFs), are generally measured at finite locations in azimuth and elevation. Thus models are needed to synthesize DTFs at finer spatial resolution than the measured data to create complete virtual auditory displays. In this research, minimum-phase all-pole and all-zero models were used for modeling both human and cat DTFs. Real cepstrum analysis has been used to represent minimum phase HRTFs in the time domain. For the human DTFs, model orders were chosen to achieve specific objective error criteria published in previous studies that were based on subjective listening tests. Because subjective listening tests are not always feasible in animals, objective methods must be used to assess the quality of the DTF reconstructions. The same error criteria reported in subjective tests of human DTF reconstructions was used to constrain models of cat DTFs on the assumption that if humans cannot discriminate reconstructed vs empirical DTFs for a given objective reconstruction error criteria, then cats won't be able to either. All-pole and all-zero models of orders as low as 25 were able to model DTFs with errors comparable to previous research findings and preserve the main spectral features in both human and cat DTFs.

A hypothesis that a systematic relation (i.e., parametric equations) can be found to describe the movements of the poles/zeros of the successful models with the change in sound source location was tested. Polynomials of different orders were extracted to describe the movements of the poles in all-pole models and zeros in all-zero models with the change in sound source location. The reconstructed DTFs were compared to the measured ones of same locations. The reconstructed DTFs preserved the main shape of the spectra, provided satisfactory RMS errors compared to the measured ones and accurately preserved the first notch spectral feature.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.


Received from ProQuest

Rights holder

Bahaa W. Al-Sheikh Hussein

File size

155 p.

File format





Biomedical engineering, Electrical engineering