Wave Field Synthesis

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Fachgebiet Audiokommunikation

Wave Field Synthesis

Marije A.J. Baalman

Institute for Audio Communication Technische Universität Berlin

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Overview

What is wave field synthesis? Possibilities and limitations The WFS system in H0104 WFS software sWONDER Assignment

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What is Wave Field Synthesis?

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Derivation wave field synthesis

y

speakers

integration line

b

source

~

r

₀

b

y

₀

~

∆

r

₀

b b

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Derivation wave field synthesis

Wave field synthesis operator (in the frequency domain):

Q(x, ω) = S(ω) s jk 2π s ∆r0 ∆r0 + r0 cos(φ0) e−jkr0 √_r 0 (1)

x is the speaker coordinate

k = ω_c , the wave number

S(ω) is the audio signal delay factor: r0

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Possibilities

Synthesize sound sources on specific places, even in front of the loudspeakers

Moving sound sources

Simulate acoustics of a room, by synthesizing reflections

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Limitations

Frequency limitations

High frequencies limited through spatial aliasing: the further apart the speakers, the lower the high frequency limit

Low frequencies limited by size of speakers

→ subwoofers!

A lot of speakers are needed!

Computation: for each speaker a signal needs to be calculated

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Spatial aliasing

f _≤ c

∆x(1 + _|sinαpw|)

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where αpw is the incidence angle with the normal on the

speaker array of the plane wave. For frequencies above this aliasing frequency, there will be components present in the wavefield with incidence angles:

sinαpw,ηal = 2π ∆xηal + ω c sinαpw ω c (3)

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Spatial aliasing

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Moving sources

Change of location over time → change of delay over time → interpolation of samples Doppler effect

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Room simulation

Simulation of the spatial reflection pattern of a room: Early reflections (up to ca. 60-100 ms)

Reverberation (from ca. 60-100 ms) Techniques:

Recording a real space using array technology

Synthesis by using mirror image sources and reverb via plane waves from different directions

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WFS in lecture hall H0104

Project part of renovation of the lecture halls, including the renewal of the media facilities

Participants:

Planning Christoph Moldrzyk

Loudspeakers Anselm Görtz, Christoph Moldrzyk Software Marije Baalman

control Simon Schampijer render Torben Hohn

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Some numbers

840-channel WFS system 2730 loudspeakers

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Hardware setup

User interface

Control PC

ETHERNET

Mixing desk Microphone

Stereo input DVD input MADI bridge

MADI

Render PC _{MADI to ADAT}

MADI speaker panel speaker panel speaker panel ADAT ETHERNET MADI cluster

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Loudspeaker panel

8 channel ADAT input

3 small speakers per channel (5.5 kHz, 10 kHz, 17kHz,

distance 10cm)

per 4 channels 1 larger spea-ker (<> 200 Hz, distance 40cm)

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Software architecture

User interface Score player

Control unit

Render unit Render unit Offline render unit Offline render unit

OSC

OSC OSC OSC OSC

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Rendering architecture

sound input

per source

direct sound

weighted delay lines (tWONDER)

+

early reflections

short convolution (fWONDER)

reverberation plane wave

8×

output

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Control unit

The control unit is the communication center for the various components.

The control unit reacts on messages from a user interface, parses these and gives subsequent

commands to the renderer and offline renderer, and informs the user interface of the current status of the system.

This is managed by various streams: render

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Current Tools

Control unit (cWONDER)

Render units (tWONDER and fWONDER) LADSPA plugin for single source control LADSPA plugin for source group control SuperCollider class

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In development

User interface (xWONDER) Score player

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OpenSoundControl

Some examples of OSC commands: /WONDER/source/position /WONDER/source/type /WONDER/source/mute /WONDER/scene/select /WONDER/scene/set /WONDER/project/load

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WFS System in the small studio

24 speakers (FOSTEX personal monitor 6301B) PC with RME Hammerfall soundcard running Linux

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Assignment

Construct a scene on the WFS system in the small studio, using Ardour and LADSPA plugins, where you show:

putting several sources on different positions using movement of some sources

adding reflections to specific sources by adding source positions (mirror image sources) and

reverb (using one of the LADSPA plugins for reverb) as plane waves

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More information

http://swonder.sourceforge.net Library of our institute

http://www.ak.tu-berlin.de (KW2)

http://www.hauptmikrofon.de/wfs.htm Google “Wave Field Synthesis”