Sound pressure equalization of audio signals using digital signal processors has been a subject of ongoing study for many years. The traditional approach is to equalize sound at a point in a listening environment, but because of its specific dependence on the room frequency response between a source and receiver position, this equalization generally causes the spectral response to worsen significantly at other locations in the room. This work presents both a time-invariant and a time-varying implementation of an adaptive acoustic energy density equalization filter for a one-dimensional sound field. Energy density equalization addresses the aforementioned challenge and others that relate to sound equalization. The theory and real-time implementation of time-invariant sound pressure and energy density equalizers designed using the least-squares method are presented, and their performances are compared. An implementation of a time-varying energy density equalizer is also presented. Time-invariant equalization results based on real-time measurements in a plane-wave tube are presented. A sound pressure equalizer results in a nearly flat spectral magnitude at the point of equalization. However, it causes the frequencies corresponding to spatial nulls at that point to be undesirably boosted elsewhere in the sound field, where those nulls do not exist at the same frequencies. An energy density equalization filter identifies and compensates for all resonances and other global spectral effects of the tube and loudspeaker. It does not attempt to equalize the spatially varying frequency nulls caused by local pressure nodes at the point of equalization. An implementation of a time-varying energy density equalizer is also presented. This method uses the filtered-x filter update to adjust the filter coefficients in real-time to adapt to changes in the sound field. Convergence of the filter over time is demonstrated as the closed end of the tube is opened, then closed once again. Thus, the research results demonstrate that an acoustic energy density filter can be used to time-adaptively equalize global spectral anomalies of a loudspeaker and a one-dimensional sound field.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


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sound equalization, acoustics, adaptive filtering, energy density, least squares, plane-wave, pressure equalization, energy density equalization, listening test, equalization history, time-adaptive filtering