A Superfast Toeplitz Matrix Inversion Method for Single- and Multi-Channel Inverse Filters and Its Application to Room Equalization

Abstract

This paper derives a superfast Toeplitz matrix inversion method using FFT techniques. The approach casts the non-periodic Toeplitz matrix solution into a periodic framework and uses the Woodbury matrix inverse identity to express the non-periodic solution as a correction to the time-windowed periodic solution. It is shown that the solution can be implemented using FFT techniques that avoid the calculation of a large matrix inverse. The method is implemented for both single- and multi-channel cases and typical computation times and accuracy are reported for the equalization of simulated and measured room impulse responses.