Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Comparison of Head-related Transfer Function Models Based on Principal Components Analysis

주성분 분석법을 이용한 머리전달함수 모형화 기법의 성능 비교

  • Published : 2008.06.20
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Abstract

This study deals with modeling of head-related transfer functions(HRTFs) using principal components analysis(PCA) in the time and frequency domains. Four PCA models based on head-related impulse responses(HRIRs), complex-valued HRTFs, augmented HRTFs, and log-magnitudes of HRTFs are investigated. The objective of this study is to compare modeling performances of the PCA models in the least-squares sense and to show the theoretical relationship between the PCA models. In terms of the number of principal components needed for modeling, the PCA model based on HRIR or augmented HRTFs showed more efficient modeling performance than the PCA model based on complex-valued HRTFs. The PCA model based on HRIRs in the time domain and that based on augmented HRTFs in the frequency domain are shown to be theoretically equivalent. Modeling performance of the PCA model based on log-magnitudes of HRTFs cannot be compared with that of other PCA models because the PCA model deals with log-scaled magnitude components only, whereas the other PCA models consider both magnitude and phase components in linear scale.

이 연구는 중앙면 상에서 주성분 분석법을 이용하여 시간 및 주파수 영역에서 머리전달함수의 모형화 기법들을 다룬다. 시간영역의 머리전달함수, 복소수 값의 머리전달함수, 확장된 머리전달함수, 로그 크기의 머리전달함수에 기반하여 각각 주성분 분석법을 수행하여 얻은 네 가지 머리전달함수 모형들에 대해서 최소자승오차 관점에서 모형화 성능을 비교하고, 모형들간의 이론적인 관계를 살펴보는 것이 이 연구의 목적이다. 모형화에 사용되는 기저함수의 수가 동일하다면, 시간영역에서의 머리전달함수 혹은 확장된 머리전달함수에 기반한 모형이 복소수 값의 머리전달함수에 기반한 모형보다 최소자승오차 관점에서 더 효율적인 모형화 성능을 지닌다. 시간영역에서의 머리전달함수에 기반한 모형과 확장된 머리전달함수에 기반한 모형은 이론적으로 동일한 모형이며 서로 푸리에 변환 관계가 있다. 로그 크기의 머리전달함수에 기반한 모형은 다른 모형들과 모형화 성능 및 이론적인 관계를 비교할 수가 없는데, 이는 로그 크기의 머리전달함수에 기반한 모형은 머리전달함수의 크기 정보만을 로그 크기로 다루는 반면에 다른 모형들은 선형 크기로 머리전달함수의 크기와 위상정보를 모두 다루기 때문이다.

Keywords

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