Head related impulse response (HRIR) is the total filtering effect induced from the reflection and diffraction of head, torso and pinna. Quaternion is a number system that extends the complex numbers. In this paper, quaternion algebra is applied to exploit the similarities among HRIRs and construct the quaternion impulse response in 7 strategies. A novel quaternion-based two-dimensional common factor decomposition is developed to decompose the quaternion-HRIRs into azimuth and elevation factors. Two datasets are used for experiments. Results show the Q-2D-CFD could achieve better performance than 2D-CFD, also, the quaternion HRTF formation strategy which exploits the front-back similarity and interaural similarity outperforms other strategies.
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