#
Auditory Distance Control Using a Variable-Directivity Loudspeaker^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Experiment I: Directivity-Controlled Auditory Distance in Auralized Rooms

- A
- the beam order i from three to zero for ${g}_{i}\left(\vartheta \right)$ and ${g}_{i}(\pi -\vartheta )$;
- B
- the ratio $a/b$ of two opposing beams: $a\text{}{g}_{3}\left(\vartheta \right)+b\text{}{g}_{3}(\pi -\vartheta )$;
- C
- the angle $\alpha $ of a beam pair: ${g}_{3}(\vartheta -\alpha /2)+{g}_{3}(\vartheta +\alpha /2)$.

#### 2.1. Experimental Setup

#### 2.2. Influence of Beampattern Design

#### 2.3. Influence of the Signal

**Figure 6.**Medians and 95% confidence intervals for tested signals ${S}_{1\cdots 3}$ in ${R}_{1}$ with beampattern design A.

#### 2.4. Influence of the Room

**Figure 7.**Medians and corresponding 95% confidence intervals for tested rooms ${R}_{1\cdots 3}$ with beampattern design A and signal ${S}_{1}$.

#### 2.5. Influence of Single-Channel Reverberation

**Figure 8.**Medians and corresponding 95% confidence intervals for reverberation levels 0, 1, 2 in ${R}_{1}$ with ${S}_{1}$ and beampattern design A.

## 3. Modeling the Auditory Distance

#### 3.1. Direct-To-Reverberant Energy Ratio

#### 3.2. Binaural Spectral Magnitude Difference Standard Deviation

#### 3.3. Inter-Aural Cross Correlation Coefficient

#### 3.4. Lateral Energy Fraction

## 4. Experiment II: Directivity-Controlled Auditory Distance in a Real Room

#### 4.1. Experimental Setup

#### 4.2. Auditory Distance

#### 4.3. Apparent Source Width

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Mason, R. How Important Is Accurate Localization in Reproduced Sound? In Proceedings of the 142th Convention of the Audio Engineering Society, Berlin, Germany, 20–23 May 2017. [Google Scholar]
- Zahorik, P.; Brungart, D.S.; Bronkhorst, A.W. Auditory distance perception in humans: A summary of past and present research. Acta Acust. United Acust.
**2005**, 91, 409–420. [Google Scholar] - Kolarik, A.J.; Moore, B.C.J.; Zahorik, P.; Cirstea, S.; Pardhan, S. Auditory distance perception in humans: A review of cues, development, neuronal bases, and effects of sensory loss. Atten. Percept. Psychophys.
**2016**, 78, 373–395. [Google Scholar] [CrossRef] [PubMed] - Mershon, D.H.; King, L.E. Intensity and reverberation as factors in the auditory perception of egocentric distance. Percept. Psychophys.
**1975**, 18, 409–415. [Google Scholar] [CrossRef] - Zahorik, P. Assessing auditory distance perception using virtual acoustics. J. Acoust. Soc. Am.
**2002**, 111, 1832–1846. [Google Scholar] [CrossRef] [PubMed] - Larsen, E.; Iyer, N.; Lansing, C.R.; Feng, A.S. On the minimum audible difference in direct-to-reverberant energy ratio. J. Acoust. Soc. Am.
**2008**, 124, 450–461. [Google Scholar] [CrossRef] [PubMed] - Kolarik, A.; Cirstea, S.; Pardhan, S. Discrimination of virtual auditory distance using level and direct-to-reverberant ratio cues. J. Acoust. Soc. Am.
**2013**, 134, 3395–3398. [Google Scholar] [CrossRef] [PubMed] - Laitinen, M.V.; Politis, A.; Huhtakallio, I.; Pulkki, V. Controlling the perceived distance of an auditory object by manipulation of loudspeaker directivity. J. Acoust. Soc. Am.
**2015**, 137, EL462–EL468. [Google Scholar] [CrossRef] [PubMed] - Wendt, F.; Frank, M.; Zotter, F.; Höldrich, R. Directivity patterns controlling the auditory source distance. In Proceedings of the 19th International Conference on Digital Audio Effects (DAFx-16), Brno, Czech Republic, 5–9 September 2016; pp. 295–300. [Google Scholar]
- Zotter, F.; Zaunschirm, M.; Frank, M.; Kronlachner, M. A Beamformer to Play with Wall Reflections: The Icosahedral Loudspeaker. Comput. Music J. (Accept. Publ.)
**2017**, 41. [Google Scholar] - Daniel, J. Représentation de Champs Acoustiques, Application à la Transmission et à la Reproduction de Scènes Sonores Complexes Dans un Contexte Multimédia. Ph.D. Thesis, Université Paris 6, Paris, France, 2001. [Google Scholar]
- Zotter, F.; Frank, M. All-round ambisonic panning and decoding. AES J. Audio Eng. Soc.
**2012**, 60, 807–820. [Google Scholar] - Allen, J.B.; Berkley, D.A. Image Method for Efficiently Simulating Small-room Acoustics. J. Acoust. Soc. Am.
**1979**, 65, 943–950. [Google Scholar] [CrossRef] - Wabnitz, A.; Epain, N.; Jin, C.T.; Van Schaik, A. Room acoustics simulation for multichannel microphone arrays. In Proceedings of the International Symposium on Room Acoustics, Melbourne, Australia, 29–31 August 2010. [Google Scholar]
- Tervo, S.; Pätynen, J.; Kuusinen, A.; Lokki, T. Spatial decomposition method for room impulse responses. J. Audio Eng. Soc.
**2013**, 61, 17–28. [Google Scholar] - Guski, R. Auditory localization: Effects of reflecting surfaces. Perception
**1990**, 19, 819–830. [Google Scholar] [CrossRef] [PubMed] - Wendt, F.; Sharma, G.K.; Frank, M.; Zotter, F.; Höldrich, R. Perception of Spatial Sound Phenomena Created by the Icosahedral Loudspeaker. Comput. Music J.
**2017**, 41, 76–88. [Google Scholar] [CrossRef] - Zaunschirm, M.; Frank, M.; Zotter, F. An Interactive Virtual Icosahedral Loudspeaker Array. Fortschritte der Akusitk
**2016**, 1331–1334. [Google Scholar] - Kohlrausch, A.; Kortekaas, R.; van der Heijden, M.; van de Par, S.; Oxenham, A.J.; Püschel, D. Detection of Tones in Low-noise Noise: Further Evidence for the Role of Envelope Fluctuations. Acta Acust. United Acust.
**1997**, 83, 659–669. [Google Scholar] - Coleman, P. Dual Role of Frequency Spectrum in Determination of Auditory Distance. J. Acoust. Soc. Am.
**1968**, 44, 631–632. [Google Scholar] [CrossRef] [PubMed] - Little, A.D.; Mershon, D.H.; Cox, P.H. Spectral content as a cue to perceived auditory distance. Perception
**1992**, 21, 405–416. [Google Scholar] [CrossRef] [PubMed] - Georganti, E.; May, T.; Van De Par, S.; Mourjopoulos, J. Sound source distance estimation in rooms based on statistical properties of binaural signals. IEEE Trans. Audio Speech Lang. Process.
**2013**, 21, 1727–1741. [Google Scholar] [CrossRef] - Marshall, A.H. A note on the importance of room cross-section in concert halls. J. Sound Vib.
**1967**, 5, 100–112. [Google Scholar] [CrossRef] - Barron, M.; Marshall, A.H. Spatial impression due to early lateral reflections in concert halls: The derivation of a physical measure. J. Sound Vib.
**1981**, 77, 211–232. [Google Scholar] [CrossRef] - Lösler, S. MIMO-Rekursivfilter für Kugelarrays. Master’s Thesis, University of Music and Performing Arts Graz, Graz, Austria, 2014. [Google Scholar]
- Zotter, F. Analysis and Synthesis of Sound-Radiation with Spherical Arrays. Ph.D. Thesis, University of Music and Performing Arts Graz, Graz, Austria, 2009. [Google Scholar]
- Kronlachner, M. Plug-in Suite for Mastering the Production and Playback in Surround Sound and Ambisonics. In Proceedings of the 136th Convention of the Audio Engineering Society, Berlin, Germany, 26–29 April 2014. [Google Scholar]
- Anderson, P.W.; Zahorik, P. Auditory/visual distance estimation: Accuracy and variability. Front. Psychol.
**2014**, 5, 1–11. [Google Scholar] [CrossRef] [PubMed] - Ernst, M.O.; Banks, M.S. Humans integrate visual and haptic information in a statistically optimal fashion. Nature
**2002**, 415, 429–433. [Google Scholar] [CrossRef] [PubMed] - Mendonça, C.; Mandelli, P.; Pulkki, V. Modeling the Perception of Audiovisual Distance: Bayesian Causal Inference and Other Models. PLoS ONE
**2016**, 11, e0165391. [Google Scholar] - Lee, H. Apparent Source Width and Listener Envelopment in Relation to Source-Listener Distance. In Proceedings of the 52nd Audio Engineering Society Conference, Guildford, UK, 2–4 September 2013. [Google Scholar]

**Figure 3.**Room and source configuration for ${R}_{1}$, ${R}_{2}$, and ${R}_{3}$ together with loudspeaker ring used for auralization. ${R}_{1}$ and ${R}_{2}$ are based on the IEM CUBE differing in the source-listener distance and room ${R}_{3}$ is based on the IEM Lecture Room.

**Figure 4.**Medians and corresponding 95% confidence intervals for all beampattern designs A, B, and C, pooled over all signals and normalized individually on directivities indicated by 1 and 7.

**Figure 5.**Direct sound and specular reflections arriving at the listening position for ${C}_{4}$ and ${C}_{7}$, normalized with respect to ${C}_{1}$.

**Figure 9.**Comparison of medians and 95% confidence intervals for all conditions (thin lines) with predictors (thick lines): D/R, BSMD STD, LF, and IACC.

**Figure 11.**Horizontal cross-section through measured frequency-dependent beampatterns of the IKO normalized by the half-octave smoothed magnitude of the loudest direction in A

^{*}

_{1}=C

_{1}. Decibel values are color coded over frequency in Hertz and azimuth angle in degree.

**Figure 13.**Experimental results of the distance task for signal ${S}_{1}$ and room ${R}_{2}$ with use of the IKO.

**Figure 14.**Medians and corresponding 95% confidence intervals for beampattern designs of assessed width for signal ${S}_{1}$ with use of the IKO.

A | ${A}_{1/7}$ | 3rd-order max-${\mathit{r}}_{\mathrm{E}}$ beam to/off listener |

${A}_{2/6}$ | 2nd-order max-${\mathit{r}}_{\mathrm{E}}$ beam to/off listener | |

${A}_{3/5}$ | 1st-order max-${\mathit{r}}_{\mathrm{E}}$ beam to/off listener | |

${A}_{4}$ | omnidirectional beampattern | |

B | ${B}_{1\cdots 7}$ | 3rd-order max-${\mathit{r}}_{\mathrm{E}}$ beams to and off listener linearly |

blended at $[\infty ,6,3,0,-3,-6,-\infty ]$ dB | ||

C | ${C}_{1\cdots 7}$ | two 3rd-order max-${\mathit{r}}_{\mathrm{E}}$ beams horizontally arranged |

at $\pm {30}^{\xb0}\text{}[0,1,\cdots 6]$ with respect to the listener |

room | ${R}_{1}$ | IEM CUBE, | $10.3\text{}\mathrm{m}\times 12\text{}\mathrm{m}\times 4.8\text{}\mathrm{m}$, | ${T}_{60}=700\text{}\mathbf{ms}$, | ${d}_{1}=1.7\text{}\mathrm{m}$ |

${R}_{2}$ | IEM CUBE, | $10.3\text{}\mathrm{m}\times 12\text{}\mathrm{m}\times 4.8\text{}\mathrm{m}$, | ${T}_{60}=700\text{}\mathbf{ms}$, | ${d}_{2}=2.9\text{}\mathrm{m}$ | |

${R}_{3}$ | IEM Lecture Room, | $7.6\text{}\mathrm{m}\times 6.8\text{}\mathrm{m}\times 3\text{}\mathrm{m}$, | ${T}_{60}=570\text{}\mathbf{ms}$, | ${d}_{3}=1.7\text{}\mathrm{m}$ | |

signal | ${S}_{1}$ | female speech taken from Music for Archimedes, CD Bang and Olufsen 101 (1992) | |||

${S}_{2}$ | sequence of irregular artificial bursts | ||||

${S}_{3}$ | speech-spectrum noise with increased kurtosis |

Set No. | Design | Index | Signal | Room | Reverb. Level |
---|---|---|---|---|---|

1 | A | $1\cdots 7$ | ${S}_{1}$ | ${R}_{1}$ | 0 |

2 | A | $1\cdots 7$ | ${S}_{2}$ | ${R}_{1}$ | 0 |

3 | A | $1\cdots 7$ | ${S}_{3}$ | ${R}_{1}$ | 0 |

4 | B | $1\cdots 7$ | ${S}_{1}$ | ${R}_{1}$ | 0 |

5 | B | $1\cdots 7$ | ${S}_{2}$ | ${R}_{1}$ | 0 |

6 | B | $1\cdots 7$ | ${S}_{3}$ | ${R}_{1}$ | 0 |

7 | C | $1\cdots 7$ | ${S}_{1}$ | ${R}_{1}$ | 0 |

8 | C | $1\cdots 7$ | ${S}_{2}$ | ${R}_{1}$ | 0 |

9 | C | $1\cdots 7$ | ${S}_{3}$ | ${R}_{1}$ | 0 |

10 | A | $1\cdots 7$ | ${S}_{1}$ | ${R}_{2}$ | 0 |

11 | A | $1\cdots 7$ | ${S}_{1}$ | ${R}_{3}$ | 0 |

12 | A | $1\cdots 7$ | ${S}_{1}$ | ${R}_{1}$ | 1 |

13 | A | $1,4,7$ | ${S}_{1\cdots 3}$ | ${R}_{1}$ | 0 |

14 | A | $1,4,7$ | ${S}_{1}$ | ${R}_{1\cdots 3}$ | 0 |

15 | A | $1,4,7$ | ${S}_{1}$ | ${R}_{1}$ | $0,1,2$ |

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**MDPI and ACS Style**

Wendt, F.; Zotter, F.; Frank, M.; Höldrich, R. Auditory Distance Control Using a Variable-Directivity Loudspeaker. *Appl. Sci.* **2017**, *7*, 666.
https://doi.org/10.3390/app7070666

**AMA Style**

Wendt F, Zotter F, Frank M, Höldrich R. Auditory Distance Control Using a Variable-Directivity Loudspeaker. *Applied Sciences*. 2017; 7(7):666.
https://doi.org/10.3390/app7070666

**Chicago/Turabian Style**

Wendt, Florian, Franz Zotter, Matthias Frank, and Robert Höldrich. 2017. "Auditory Distance Control Using a Variable-Directivity Loudspeaker" *Applied Sciences* 7, no. 7: 666.
https://doi.org/10.3390/app7070666