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  • Publication
    Open Access
    Spatial Audio Through Headphones Based on HRTFs Approximated by Parametric IIR Filters
    (Universitätsbibliothek der HSU / UniBwH, 2022-06) ; ;
    Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg
    The subject of this dissertation is spatial audio through headphones. In the present work, an offline binaural synthesis implementation is proposed using head-related transfer functions (HRTFs) approximated by cascades of parametric infinite impulse response (IIR) filters, parameter interpolation to calculate HRTFs of intermediate directions for generating static as well as moving virtual sound sources, and simulated room effects in order to increase the perceived externalization. The first contribution to the research field lies in representing HRTFs as cascades of low-order parametric IIR filters together with a delay representing the interaural time difference (ITD). Usually, HRTFs are represented as finite impulse response (FIR) filters containing the corresponding head-related impulse responses (HRIRs) as filter coefficients. However, by using cascades of low-order parametric IIR filters, like first-order shelving or second-order peak filters, memory requirements of the used hardware can be decreased to three parameters per filter stage (cut-off or center frequency, gain, and Q-factor). For this purpose, a two-step procedure is proposed that approximates the magnitude responses of HRTFs by parametric IIR filter cascades. In a first step, the individual filter stages are consecutively integrated, initialized, and tuned. Afterwards, the interaction between individual filter stages is post-optimized. Alternatively, an approach for HRTF magnitude response approximation based on instantaneous backpropagation is proposed. After approximating the HRTF magnitude responses, also the ITDs have to be extracted from the HRIRs or HRTFs of the two ears. From this, virtual sound sources are generated by filtering a monaural audio signal with the parametric IIR filter cascades of the desired direction and delaying the filtered audio signal of the contralateral ear by the extracted ITD. In many practical implementations, only a finite number of measured HRTFs is available, resulting in a limited spatial resolution. For HRTFs represented as FIR filters, bilinear rectangular or triangular interpolation can be used to calculate the filter coefficients of intermediate HRTFs. However, when the HRTFs are represented as IIR filters instead, the interpolation is not as straightforward as for FIR filters due to stability considerations. Therefore, in this work, a parameter interpolation algorithm based on bilinear interpolation of the parameters of the individual filter stages together with an assignment of related peak filters is proposed. This interpolation algorithm guarantees the stability of intermediate filters. When generating moving virtual sound sources, two IIR filter cascades are combined in parallel following the cross-fading input-switching combination approach. For evaluating the proposed methods, three listening tests assessing different aspects of binaural synthesis using HRTFs approximated by parametric IIR filters are performed. In a first listening test, the validity of the proposed parametric IIR filter cascades is proven for static virtual sound sources by comparing their localization results to localization results achieved using HRIRs represented as FIR filters. Additionally, a second listening test proves that adding simulated room effects via the image source model increases the perceived externalization of static virtual sound sources generated using HRTFs approximated by parametric IIR filter cascades up to externalization levels achieved using measured binaural room impulse responses represented as FIR filters. Finally, the audio quality of moving virtual sound sources generated using minimum-phase approximated HRIRs represented as FIR filters and parametric IIR filter cascades is evaluated in a third listening test. By using two IIR filters in parallel following the cross-fading input-switching combination approach, comparable audio quality ratings are achieved as for FIR filter implementations using minimum-phase approximated HRIRs. Thus, HRTFs approximated by parametric IIR filter cascades can be used to reduce the number of saved coefficients. By using two first-order shelving filters, ten second-order peak filters, a mean HRTF magnitude value, and an extracted ITD, only 36 parameters have to be saved per HRTF instead of 200 coefficients as in FIR filter implementations using conventional HRIRs.
  • Publication
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