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Spatial Audio Concepts

This section briefly introduces key concepts used throughout the Binaural Rendering Toolbox (BRT).
The goal is not to provide a full theoretical treatment, but to give enough background to understand how these concepts are used within the BRT framework.

For deeper explanations, external references are provided for each concept.

A Head-Related Transfer Function (HRTF) describes how an incoming sound wave is filtered by a listener's head, torso, and outer ears (pinnae) before reaching the eardrums. These filtering effects depend on the direction and distance of the sound source, and they provide the cues that allow humans to perceive sound spatially.

In practice, HRTFs are usually represented as a set of Head-Related Impulse Responses (HRIRs). Each HRIR captures the acoustic response from a specific source position to the listener's left and right ears.

Measurement directions are typically described using:

  • Azimuth (horizontal angle around the listener)
  • Elevation (vertical angle)
  • Distance from the listener

When an audio signal is convolved with the HRIR corresponding to a specific direction, the resulting signal reproduces the spatial filtering cues that make the sound appear to originate from that location.

flowchart LR
    Source[Sound Source]
    Propagation[Sound Propagation]
    Head[Head / Torso / Pinnae Filtering]
    LeftEar[Left Ear Signal]
    RightEar[Right Ear Signal]
    Brain[Spatial Perception]

    Source --> Propagation
    Propagation --> Head
    Head --> LeftEar
    Head --> RightEar
    LeftEar --> Brain
    RightEar --> Brain

HRTFs in BRT

The BRT framework represents HRTFs as collections of HRIRs associated with spatial coordinates (azimuth, elevation, and distance).

The system is designed to support arbitrary distributions of measurement directions, meaning that it does not require a regular spherical grid and does not impose minimum spatial density constraints.

This flexibility allows BRT to work with a wide range of existing HRTF datasets.

External references

A Head-Related Impulse Response (HRIR) is the time-domain representation of the HRTF for a specific spatial direction.

Each HRIR corresponds to the impulse response measured between a sound source located at a given position and the listener's ears. In binaural audio systems, two HRIRs are typically recorded for each measurement direction:

  • one for the left ear
  • one for the right ear

HRIRs are usually measured using dummy heads or real listeners equipped with miniature microphones placed at the ear canals.

In binaural rendering systems, spatial audio is generated by convolving the input signal with the HRIR pair corresponding to the source direction.

External references

Binaural Room Impulse Response (BRIR)

A Binaural Room Impulse Response (BRIR) extends the concept of HRIR by including the acoustic effects of an environment.

While an HRIR models only the filtering caused by the listener's anatomy, a BRIR also includes:

  • early reflections from room surfaces
  • late reverberation
  • the interaction between the listener and the room acoustics

A BRIR therefore captures the complete acoustic response between a sound source and the listener in a particular environment.

BRIRs are widely used in spatial audio rendering systems to reproduce realistic acoustic environments over headphones.

External references

Ambisonics

Ambisonics is a spatial audio representation technique that encodes a sound field using spherical harmonics. Instead of representing audio as signals tied to specific loudspeakers, ambisonics represents the entire sound field around a listener.

This representation has several advantages:

  • the sound field can be rotated or manipulated mathematically
  • it can be decoded to different playback systems
  • it supports efficient spatial audio processing

In binaural rendering systems, ambisonic signals are typically converted to binaural signals through a binaural decoding stage, which uses HRTFs or ambisonic-domain impulse responses.

External references