Talk:SOFA specifications: Difference between revisions
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SimpleFreeFieldSOS : Simple Free Field Second Order Sections |
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Here we can discuss Thibaut's suggestion to create a new data type. |
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==Description== |
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This convention is essentially the same as SimpleFreeFieldHRIR except that it is adapted to a parametric model of HRIR. |
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This parametric model consists of replacing HRIR (as FIR) with a monaural delay and second order sections filters. |
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==Background== |
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Being a causal and stable filter, an HRIR can be decomposed into a minimum phase part component and an all-pass component. |
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The phase of each HRIR is thus decomposed into the minimum phase and the phase of the all-pass component i.e. the excess phase. |
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The minimum phase is related to the magnitude spectrum through the Hilbert transform. |
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The excess phase of HRIR is usually linear (up to approx 8 - 10 kHz). |
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A simplified model of HRTF can thus be built where the all-pass component is replaced by a pure delay. This pure delay is referred to as monaural delay. |
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Each HRTF is thus fully described by its magnitude spectrum and the monaural delay. |
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Several perceptual studies (Wightman 1992) have shown the validity of such simplified model (given the fact that the phase information of the higher frequencies -- that is neglected by the model -- is not used by the auditory system to estimate the directions of arrival). |
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Finally the minimum phase part of HRTF can be modeled as an IIR filter. Many modeling techniques have been proposed. Anyway the resulting IIR digital filter needs to be represented as a cascade of first order or second order sections for numerical stability reasons. |
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Revision as of 15:25, 13 October 2014
SimpleFreeFieldSOS : Simple Free Field Second Order Sections
Description
This convention is essentially the same as SimpleFreeFieldHRIR except that it is adapted to a parametric model of HRIR. This parametric model consists of replacing HRIR (as FIR) with a monaural delay and second order sections filters.
Background
Being a causal and stable filter, an HRIR can be decomposed into a minimum phase part component and an all-pass component. The phase of each HRIR is thus decomposed into the minimum phase and the phase of the all-pass component i.e. the excess phase. The minimum phase is related to the magnitude spectrum through the Hilbert transform. The excess phase of HRIR is usually linear (up to approx 8 - 10 kHz). A simplified model of HRTF can thus be built where the all-pass component is replaced by a pure delay. This pure delay is referred to as monaural delay. Each HRTF is thus fully described by its magnitude spectrum and the monaural delay. Several perceptual studies (Wightman 1992) have shown the validity of such simplified model (given the fact that the phase information of the higher frequencies -- that is neglected by the model -- is not used by the auditory system to estimate the directions of arrival). Finally the minimum phase part of HRTF can be modeled as an IIR filter. Many modeling techniques have been proposed. Anyway the resulting IIR digital filter needs to be represented as a cascade of first order or second order sections for numerical stability reasons.