Chameleon subwoofer arrays - Adam J. Hilladamjhill.com/AJHILL/wp-content/uploads/2017/05/AES-UK-2011.pdf · Chameleon subwoofer arrays ... Virtual bass systems 7. Extended CSA applications

Chameleon subwoofer arrays

Adaptable loudspeaker polar responses for improved control in the low-frequency band

Adam Hill

Audio Research Laboratory

School of Computer Science & Electronic Engineering

University of Essex, Colchester, UK

11 October 2011

Problem statement

Develop a low-frequency sound reproduction

system capable of delivering a consistent spectral

and temporal response across a wide-area.

Presentation outline

1. Low-frequency room acoustics

2. Acoustical modeling

3. Simulation toolbox development

4. Conventional low-frequency room correction

5. Chameleon subwoofer arrays (CSA)

6. Virtual bass systems

7. Extended CSA applications









Low-frequency room acoustics [1/5]

• What is “low-frequency”?

• Depends on the room

• Schroeder frequency

• Example:

• V = 8 x 5 x 3 m = 120 m3

• T60 = 0.5 second

𝑓𝑠 = 2000 𝑇60

𝑉

𝑓𝑠 = 2000 0.5

120≈ 129 𝐻𝑧


• Room modes

• Half-wavelength integer multiples of one or more room dimension

• Result = standing wave pattern

Axial Mode Tangential Mode Oblique Mode


• Measurements

• 25 separate listening locations

Frequency response measurements 80 Hz tone burst measurements


• Metrics – spatial variance (SV)

• How much does the frequency response vary over the listening area?

where: SV = spatial variance (dB)

Nf = number of frequency bins

Np = number of listening locations

flo, fhi = frequency range (Hz)

Lp(p,i) = sound pressure level (dB) at listening location,

p, and frequency bin, i

Lp(i) = mean sound pressure level (dB) over all

listening locations at frequency bin, i

𝑆𝑉 =1

𝑁𝑓

1

𝑁𝑝 − 1 𝐿𝑝 𝑝, 𝑖 − 𝐿𝑝 𝑖

2

𝑁𝑝

𝑝=1

𝑓ℎ𝑖

𝑖= 𝑓𝑙𝑜


• Metrics – mean output level (MOL)

• What is the average output amplitude over the listening area?

where: MOL = mean output level (dB)

Nf = number of frequency bins

Np = number of listening locations

flo, fhi = frequency range (Hz)

Lp(p,i) = sound pressure level at listening location, p, and

frequency bin, i

𝑀𝑂𝐿 =1

𝑁𝑓𝑁𝑝 𝐿𝑝 𝑝, 𝑖

𝑁𝑝

𝑝=1

𝑓ℎ𝑖

𝑖=𝑓𝑙𝑜









Acoustical modeling [1/4]

• Finite-Difference Time-Domain (FDTD)

• Why?

• Computationally efficient (at LF, at least)

• Low-frequency accuracy

• Straightforward to implement

• Goals

• Create a flexible acoustics toolbox

• Adequate data analysis/animation options

• Examine room-mode correction methods

• Virtually prototype novel correction routine

• OR...


• Make some interesting abstract art


• FDTD – how does it work?


• FDTD – non-rectangular topologies?

• Common techniques – grid discretization

• Circular space (2D example)

• Red dots = pressure elements

Simple Quasi-Cartesian Locally-conformal









Simulation toolbox development [1/5]


• Validation – theoretical room-modes (spectral distribution)

𝑓𝑚 =𝑐

2

𝜂𝑥𝐿𝑥

2

+ 𝜂𝑦𝐿𝑦

2

+ 𝜂𝑧𝐿𝑧

2


• Validation – theoretical room-modes (spatial distribution)

Axial Tangential Oblique


• Validation – measurements (old Essex Audio Research Lab)

1 subwoofer, room corner 2 subwoofers, front room corners


• Validation – previously published results

• Welti & Devantier – JAES vol. 54, no. 5, pp. 347-364. May 2006.

We

lti

FD

TD

To

olb

ox

1 subwoofer, room corner









Conventional correction [2/8]

• Absorption

• Foam blocks, bass traps, specialized surface material

• Difficult to achieve over entire subwoofer band

Frequency response for surface absorption of 2% (left) and 20% (right)


• Single subwoofer placement

Spatial variance (dB) for various subwoofer positions


• Multiple subwoofer placement

4 subwoofers at wall midpoints 5,000 subwoofers randomly placed


• Active equalization methods

• Single point or multiple point

• Static or adaptive

• Alternatively, manual methods (parametric/graphic EQ)

Pre-EQ (red = target point) Post-EQ (red = target point)


• Polar pattern control

• Gradient loudspeakers (Olson)

• Dual-pattern subwoofers (Backman)

• Lower subwoofer band = omnidirectional

• Upper subwoofer band = cardioid

Dual pattern subwoofer configurations


• Alternative methods

• Room dimensions

• Walker – 100th AES Convention, paper 4191. May, 1996.

• Milner – JASA, vol. 85, no. 2, pp. 772-779. February, 1989.

• Active absorption

• Vanderkooy – 123rd AES Convention, paper 7262. October, 2007.

• Celestinos – 120th AES Convention, paper 6688. May, 2006.

• Radiation resistance

• Pedersen – 115th AES Convention, paper 5880. October, 2003.

• Ambisonics-style equalization

• Howe + Hawksford – 91st AES Convention, paper 3138. October, 1991.









Chameleon subwoofer arrays [1/13]

• Four source components

(hybrid subwoofer)

• S1 = omni, S2 = x-dipole,

S3 = y-dipole, S4 = z-dipole

• H = filter coefficients matrix

• X = measured response matrix

• Y = target response matrix

S1 S2 S3 S4

L1 L2 L3 L4

𝐻𝑁𝑆𝑥1 = 𝑋𝑁𝐿𝑥𝑁𝑆−1 𝑌𝑁𝐿𝑥1


• System practicality issues

• Multi-band operation (dipole efficiency)

• Lower correction limit

• Upper correction limit

• Windowing

Correction filter ringing Proper correction filters


• Target point correction (simulated)

• 1 unit CSA (single hybrid subwoofer)

• 4 degrees of freedom = 4 target points

System configuration Frequency responses

Uncorr

ecte

d

Corr

ecte

d

88% spatial variance reduction


• Walking path correction (simulated)




Uncorr

ecte

d

Corr

ecte

d



• Walking path correction (simulated)

• 4 unit CSA (four hybrid subwoofers)



Uncorr

ecte

d

Corr

ecte

d



• Hybrid vs. conventional subwoofers in CSAs

• 16 degrees of freedom

Hyb

rid

Conventional

Uncorrected Corrected

SV reduction = 93.9%

SV reduction = 88.6%


• Source position offset


60% SV reduction

40% SV reduction

20% SV reduction


• Vertical correction range

• 4 unit CSA (four hybrid subwoofers)

2D (horizontal) target

point distribution

3D target point

distribution

Correction area:

6.6 m2

Correction volume:

5.4 m3


• Pseudo-inverse filtering

• target points > degrees of freedom

• Improved spatial sampling (2m x 2m listening area tested)

0

20

40

60

80

100

4 9 16 25 36 49 64 81 100Spat

ial

vari

ance

re

du

ctio

n

(%)

Target measurement points

1 unit

2 units

3 units

4 units

2.0 m spacing 0.2 m spacing

0.6 m spacing = accurate spatial sampling up to ~140 Hz


• CSA prototype

• Conventional subwoofer 4-unit array

• Walking path over 1.8m x 1.8m listening area

• Experimental results compared to simulations

Uncorr

ecte

d

Corr

ecte

d

Measurements Simulations

SV reduction = 69% SV reduction = 80%


• CSA prototype

• Hybrid subwoofer development

• Stage 1: LF polar pattern control

• Undergraduate final-year project

• 55cm cubed... very problematic!


• CSA prototype

• Hybrid subwoofer development

• Stage 2: CSA implementation

• Redesigned from stage 1

• 44cm cubed... much better!


• CSA prototype

• Hybrid subwoofer 1-unit array

• Walking path over 1.8m x 1.8m listening area

• Experimental results compared to simulations

(source components not a direct match)

Uncorr

ecte

d

Corr

ecte

d

Measurements Simulations

SV reduction = 51% SV reduction = 82%









Virtual bass systems [1/6]

• Chameleon subwoofer array problems

• 1 or 2 problematic narrow frequency bands

• Filter ringing + unrealistic amplitude requirements

• Goals

• Eliminate need for physical reproduction at problematic frequencies

• Subjectively reinforce correction systems

Original CSA correction coefficients Adjusted CSA correction coefficients


• Principle of the missing fundamental

• Psychoacosutical effect

• Harmonic components = perception of fundamental

• Existing applications

• Loudspeaker/headphone bandwidth extension

• Bass boost

• Implementation approaches

• Time domain

• Frequency domain

• Time/frequency hybrid

• Hybrid NLD + PV system

• Output mixing defined by input content

• Transient content detector (TCD)

• Advantages

• Less input sensitivity

• Acceptable transient + steady-state performance

• Disadvantages

• Computational complexity

• Best case scenarios not as good as pure NLD/PV systems


• PEQ = parametric equalization

• BPF = bandpass filter

• VB = virtual bass processing

• G = gain


6.0

5 m

5.79 m

1.50 m

3.5

5 m

4

.25

m

4.79 m

1.8

0 m

4

.25

m

5.5

5 m

0

.50

m

2.90 m

L

R

= listening location

= subwoofer

= main loudspeaker


Good

Fair

Poor

Significant

None

Moderate










Extended CSA applications [1/6]

• Individualized response manipulation

• CSA default response at all locations

• Each listener can adjust local response in real-time

Uncorr

ecte

d

CS

A c

orr

ecte

d

(defa

ult r

esponse)


• Individualized response manipulation

1. 72 Hz cut

2. 72 Hz cut, 60 Hz cut, 80 Hz boost

• ~ 2 dB output loss for each manipulation

Manip

ula

tion

#1

Manip

ula

tion

#2

Before

After


• Live sound reinforcement

• Goals

• Even audience coverage

• Minimal stage SPL

• Conventional approaches

• Cardioid subwoofers

• Subwoofer spacing

• Subwoofer clusters

• CSA implementation

• Utilize existing system degrees of freedom

• Audience + stage measurement points

• Two zones of “individualized” correction


• Live sound reinforcement

• Example system: 8 cardioid subwoofers (16 degrees of freedom)

Sys

tem

layo

ut

Covera

ge p

attern

Uncorrected 16 measurement points 100 measurement points


• Surround sound systems

• Fit within existing hardware

• Utilize low-frequency capabilities of

each loudspeaker

• Are LF directional cues important?


• Surround sound systems

• Non-subwoofer cutoff: 62 Hz

Uncorrected

Corrected


Conclusions

• Chameleon subwoofer arrays

• Advantages • Minimal spatial variance over wide-area

• Accurate transient response

• Disadvantages • New hardware

• Calibration measurements

• Solutions + alternative implementations

• Virtual bass subjective reinforcement

• Individualized frequency response control

• DSP within surround/live sound systems

Future work

• Hybrid subwoofers

• Drive-unit cross-talk

• Low-frequency extension?

• Chameleon subwoofer array DSP

• Refine window selection procedure

• Problematic filter identification

• System experimentation

Questions?

FDTD + virtual bass software free to download at

www.adamjhill.com

Chameleon subwoofer arrays - Adam J. Hilladamjhill.com/AJHILL/wp-content/uploads/2017/05/AES-UK-2011.pdf · Chameleon subwoofer arrays ... Virtual bass systems 7. Extended CSA applications

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