HRTF Order Reduction via Balanced State Space

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Solution Overview

Problem

Conventional binaural rendering methods require large computational resources due to the need for 2M filter operations, which can tax limited resources in virtual reality applications, especially when using finite impulse response (FIR) filters for Head Related Transfer Functions (HRTFs).

Innovation Solution

The method involves applying a balanced-realization state space model to reduce the order of HRTFs, converting them from FIR to Infinite Impulse Response (IIR) filters, and using state space reduction techniques to truncate the system, resulting in a more efficient representation that approximates the original HRTF with a significant reduction in computational requirements, up to 90% less.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If conventional FIR filters are used for HRTF in binaural rendering, then audio fidelity is maintained, but computational resources are heavily taxed

Engineering Contradiction:
Improveaudio fidelityVSAvoidcomputational resources
Core Design Contradiction:
Measurement precisionVSDevice complexity

Solution Approach 1:

The patent transforms the HRTF filter type from FIR to IIR, fundamentally changing the filter parameter structure. This allows representing the same audio transfer function with fewer parameters (lower order), reducing computational complexity while maintaining audio fidelity through the mathematical equivalence of the transformed IIR filter to the original FIR filter

Inventive Principle:
Principle #35Parameter changes

Solution Approach 2:

The patent creates a simplified copy of the HRTF system using IIR filters that replicates the acoustic transfer function behavior. By copying the essential characteristics of the original FIR-based HRTF into a more efficient IIR representation, the system achieves the same audio rendering quality with reduced computational load

Inventive Principle:
Principle #26Copying

2Measurement precision

If the number of virtual loudspeakers M is increased to improve spatial audio quality, then audio rendering quality improves, but the number of filter operations increases to 2M

Engineering Contradiction:
Improvespatial audio qualityVSAvoidprocessing efficiency
Core Design Contradiction:
Measurement precisionVSProductivity

Solution Approach 1:

By changing the filter type from FIR to IIR, the patent reduces the effective order of each filter. This parameter change means that even as M increases to improve spatial quality, the computational burden per filter is significantly reduced, improving overall processing efficiency

Inventive Principle:
Principle #35Parameter changes

Solution Approach 2:

The patent introduces adaptive order reduction that can dynamically adjust the complexity of the IIR filter representation. This allows the system to optimize the balance between spatial audio quality and processing efficiency based on real-time computational resource availability

Inventive Principle:
Principle #15Dynamics

Data Source

PatentEP3351021B1Signal processing methods and systems for rendering audio on virtual loudspeaker arrays
Publication Date: 2020.04.08 GOOGLE LLC
  • EP3351021B1 patent drawingFigure 1
  • EP3351021B1 patent drawingFigure 2
  • EP3351021B1 patent drawingFigure 3

AI summary

Techniques of rendering audio involve applying a balanced-realization state space model to each head-related transfer function (HRTF) to reduce the order of an effective FIR or even an infinite impulse response (IIR) filter. Along these lines, each HRTF G(z) is derived from a head-related impulse response filter (HRIR) via, e.g., a z-transform. The data of the HRIR may be used to construct a first state space representation [A,B, C, D] of the HRTF via the relation G(z) = c(zl - A) -1 B + D. This first state space representation is not unique and so for an FIR filter, and may be set to simple, binary-valued arrays, while C and D contain the HRIR data. This representation leads to a simple form of a Gramian Q whose eigenvectors provide system states that maximize the system gain as measured by a Hankel norm. Further, a factorization of Q provides a transformation into a balanced state space in which the Gramian is equal to a diagonal matrix of the eigenvalues of Q. By considering only those states associated with an eigenvalue greater than some threshold, the balanced state space representation of the HRTF may be truncated to provide an approximate HRTF that approximates the original HRTF very well while reducing the amount of computation required by as much as 90%.