Quaternion common factor decomposition of head-related impulse response

The hypercomplex number quaternion is an extension to the complex number and is widely used in computer graphic, image processing and multiple dimensional linear time-invariant systems. In this paper, the quaternion algebra is applied to head-related impulse response (HRIR) modeling. Four HRIRs measured at different elevations or for different ears are used to construct a quaternion impulse response. A two dimensional quaternion common factor decomposition (QCFD) algorithm is developed to represent each quaternion impulse response as the convolution of two factor impulse responses. By using the proposed QCFD algorithm, quaternion impulse responses with the same elevation will share the same elevation factor while quaternion impulses with the same azimuth will share the same azimuth factor. Experimental results show that the QCFD algorithm has better performance as compared to the traditional two-dimension common factor decomposition (CFD) algorithm.