Exploiting randomness in acoustic impulse responses to achieve headphone compensation through deconvolution

Abstract

This paper presents a method of headphone/earphone equalization based upon deconvolution of the headphone impulse response from other acoustic filters in the processing chain. The methods presented are thus applicable to areas such as spatial audio, where input signals are processed with binaural impulse responses. The extraction of low order from higher order acoustic impulse responses is justified based upon an application of the theory pertaining to the clustering of the zeros of random coefficient polynomials about the unit circle. An argument is presented supporting the applicability of this theory to acoustic impulse responses. Such an equalization method guarantees a considerable reduction in computational effort over traditional separate compensating filters. A comparison is presented of the implementation of the equalization using the homomorphic method and least squares method with and without regularization to a traditional separate least squares inverse filter. The proposed approach is shown to have a performance comparable to a separate least squares designed compensator, often giving superior performance despite a large reduction in complexity.

Phase and Randomness in Acoustic Responses

“…The tail of an acoustic impulse can be modelled as a decaying random coefficient polynomial [5] [6]. Random coefficient polynomials have been shown to exhibit zeros which cluster uniformly about the unit circle.…”

“…Figure 5 demonstrates this error. This is due to the matching of the log magnitude frequency responses of these sequences at a small number of points, in this case 5 In the case of responses whose zeros are very close to or on the unit circle, such as HRIRs and RIRs as discussed in Section II, there are additional issues regarding the calculation of the inverse cepstrum. When there are zeros lying very close to or on the unit circle, the magnitudes of the Fourier coefficients at the corresponding frequencies will be very close to zero.…”