*(under construction)*

This page provides audio examples that illustrate the significance of the information in a sound field at high spherical harmonic (SH) orders at low frequencies on the signals that arise at the ears of a human who is exposed to the sound field. The sound fields considered here are spherical waves that originate from different distances. The HRTFs of the listener are imposed on the SH representation of the sound field (a.k.a. binaural rendering) to compute the binaural signals. We use the HRTFs of a rigid spherical head that has a radius of 0.075 m. For convenience, we limit the SH representation to 10th order.

The *ground truth* always comprises the SH representation of the sound field being rendered binaurally as is. The difference with the *array* stimuli compared to the ground truth is that the SH coefficients of the sound field are attenuated at low frequencies in the same way a spherical or equatorial microphone array would attenuate them as a consequence of the regularization of the radial filters. The smaller the array radius is, the stronger is the attenuation and the higher in frequency does it reach. Note that, although we emulated microphone arrays, the signals do not comprise any spatial aliasing. What we emulate is only the attenuation of the modes of the SH representation of the sound field.

All audio examples on this page are binaural. It is therefore utterly important that you listen to them via **headphones**.

The attenuation of the SH modes emulates radial filters confined to a dynamic range of 40 dB. fc is the frequency above which a given mode is apparent with no attenuation in the binaural signals of type ‘array’.

Source direction: straight ahead. Array radius: 0.2 m

SH modes are available above 0 Hz (n = 0), 100 Hz (n = 1), 300 Hz (n = 2), etc.

Source Distance | Ground Truth | Array |

3 m | ||

1 m | ||

0.3 m |

Source direction: 90° on the right. Array radius: 0.2 m

SH modes are available above 0 Hz (n = 0), 100 Hz (n = 1), 300 Hz (n = 2), etc.

Source Distance | Ground Truth | Array |

3 m | ||

1 m | ||

0.3 m |

Source direction: straight ahead. Array radius: 0.1 m

SH modes are available above 0 Hz (n = 0), 200 Hz (n = 1), 600 Hz (n = 2), etc.

Source Distance | Ground Truth | Array |

3 m | ||

1 m | ||

0.3 m |

Source direction: 90° on the right. Array radius: 0.1 m

SH modes are available above 0 Hz (n = 0), 200 Hz (n = 1), 600 Hz (n = 2), etc.

Source Distance | Ground Truth | Array |

3 m | ||

1 m | ||

0.3 m |

Source direction: straight ahead. Array radius: 0.05 m

SH modes are available above 0 Hz (n = 0), 400 Hz (n = 1), 1200 Hz (n = 2), etc.

Source Distance | Ground Truth | Array |

3 m | ||

1 m | ||

0.3 m |

Source direction: 90° on the right. Array radius: 0.05 m

SH modes are available above 0 Hz (n = 0), 400 Hz (n = 1), 1200 Hz (n = 2), etc.

Source Distance | Ground Truth | Array |

3 m | ||

1 m | ||

0.3 m |