Applications of least-squares FIR filters to virtual acoustic space

A virtual acoustic space (VAS) employs the localization cues specified by the direction-dependent 'free-field to eardrum transfer function' (FETF) to synthesize sound-pressure waveforms present near the tympanum. The combination of a VAS and the earphone delivery of synthesized waveforms is useful to study parametrically the neural mechanisms of directional hearing. The VAS-earphone procedure requires accurate FETF estimation from free-field measurements and appropriate compensation for the undesirable spectral characteristics of the closed-field earphone sound delivery and measurement systems. Here we describe how specially designed finite-impulse-response (FIR) filters improve these two operations. The coefficients of an FIR filter are determined using a least-squares error criterion. The least-squares FIR filter is implemented entirely in the time domain and avoids the usual problems with division inherent in a frequency domain approach. The estimation of an FETF by a least-squares FIR filter is veracious since its impulse response can recover signals that were recorded near the eardrum in the free field with a very high fidelity. The correlation coefficient between recorded and recovered time waveforms typically exceeds 0.999. Similarly, least-squares FIR filters prove excellent in compensating closed-field sound systems since comparisons of waveforms delivered by a compensated earphone to their corresponding predistorted signals yield correlation coefficients that exceed 0.99 on average.