Experimental Equalization of a One-Dimensional Sound Field Using Energy Density and a

Parametric EqualizerMicah Shepherd, Xi Chen, Timothy W. Leishman,

Scott D.Sommerfeldt

Acoustics Research GroupDepartment of Physics and Astronomy

Brigham Young University

148th Meeting of the Acoustical Society of America18 November 2004

Background and Traditional Technique

• Background– Sound fields in rooms do

not have ideal responses– Sound field equalization

compensates for room effects using filters

• Traditional techniques– Excite room using pink

noise– Measure pressure

response at one location– Cut and boost in nth octave

bands using graphic equalizer to produce desired response

• Better control using parametric equalizers– Variable frequency– Variable Q

• Problems– Spatial variance of sound

field– Microphone at nodes– Limited frequency and gain

adjustment• Need for a better

approach

Search for an Improved Technique

• Measure transfer function between source and receiver in 1-D sound field

• Three cases– Single point mean-squared pressure– Spatially averaged mean-squared pressure

(potential energy density)– Single point total energy density

• Use normalized inverses of the responses as equalization filters

Experimental Setup

Energy Density

• Pressure gradient method

Estimate particle velocity using

pressure gradient

Energy Density is then

• 2 microphone transfer function method

Developed by Chung and Blaser

Solve for incident and reflected pressure and reflection coefficients at microphone positions

Derive particle velocity and energy density from result

)(1

120

ppxj

u

])/([2

1 20

20 cpuED

Difference in ED Estimations

0 200 400 600 800 1000 1200 1400 16000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1N

orm

aliz

ed E

D

Frequency Hz

Pressure Gradient2 mic transfer Func Method

Unequalized FieldMean-Squared Pressure Field Energy Density Field

Ideal Inverse Filters From Measured Field

0 200 400 600 800 1000 1200 1400 16000

10

20

30

40

50

f

Field Pressure

Point E. D.

Term. Pressure

Spat. Av. Pressure

Ideal Equalized Pressure Fields

Mean-Squared Pressure EQ Energy Density EQ

0 200 400 600 800 1000 1200 1400 1600-40

-35

-30

-25

-20

-15

-10

-5

0

Frequency Hz

Parametric Equalizerideal

Comparison of Ideal Energy DensityFilter and Parametric EQ Filter

Equalized Pressure Fields

80100120

25

50

70

0

0

400

800

1200

1600

Hz

cm

dB80100120

25

50

70

0

0

400

800

1200

1600

Hz

cm

dB

Parametric ED EQ Ideal ED EQ

200 400 600 800 1000 1200 1400 160020

25

30

35

40

45

50

Frequency Hz

Parametric EqualizerIdeal Energy Density filter

Spatially Averaged Pressure Responses: Ideal and Parametric

Conclusions

• Energy density equalization approximates spatially averaged pressure equalization in a 1-D sound field

• A discrete ED measurement can be used to equalize a 1-D sound field better than a discrete pressure measurement

• Parametric equalizers can be used to approximate ideal ED filters, but with notable errors

Future work

• Conduct more general tests in a 1-D field with variable side-branch source positions

• Test energy density equalization methods in 3-D sound fields

• Test energy density equalization methods using multiple sources

• Develop adaptive filtering techniques

Thank you