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

1. Experimental Equalization of a One-Dimensional Sound Field Using Energy Density and a Parametric Equalizer Micah Shepherd, Xi Chen, Timothy W. Leishman, Scott D.Sommerfeldt Acoustics Research Group Department of Physics and Astronomy Brigham Young University 148th Meeting of the Acoustical Society of America 18 November 2004

2. 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 Background and Traditional Technique

3. 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

4. Experimental Setup

5. 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 Energy Density

6. Difference in ED Estimations

7. Unequalized Field Mean-Squared Pressure Field Energy Density Field

8. Ideal Inverse Filters From Measured Field

9. Ideal Equalized Pressure Fields Mean-Squared Pressure EQ Energy Density EQ

10. Comparison of Ideal Energy Density Filter and Parametric EQ Filter

11. Equalized Pressure Fields Parametric ED EQ Ideal ED EQ

12. Spatially Averaged Pressure Responses: Ideal and Parametric

13. 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

14. 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

15. Thank you