Download - Micah Shepherd, Xi Chen, Timothy W. Leishman, Scott D.Sommerfeldt Acoustics Research Group
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