Equalizer of Amplitude-Frequency Response of Acoustic Channels and its Adaptive Filter Based on Recursive Least Squares Algorithm with Diagonalized Correlation Matrix

Abstract

The paper presents an equalizer of the amplitude-frequency response of the acoustic wave propagation channels in the rooms. The considered equalizer uses the so-called modified architecture based on the adaptive filter with the input signal filtering, which weights are calculated using the Recursive Least Squares (RLS) algorithm. The equalizer of the acoustic channels amplitude-frequency response usually requires the usage of the adaptive filters with the large number of weighs that means the large computational complexity of the adaptive filter. The adaptive filters based on the fast RLS algorithms are efficient in the terms of their complexity but often unstable if the number of adaptive filter weights is large. Therefore, the algorithms are poorly suited for usage in the amplitude-frequency response equalizers of the acoustic channels. Adaptive filters based on the RLS algorithm, which use the Matrix Inversion Lemma (MIL), are stable, but computationally complex. The equalizer presented in this paper uses a simplified adaptive filter based on the MIL RLS algorithm with a diagonalized correlation matrix of the filter input signal. In addition, in the filter, each of the square submatrices on the simplified correlation matrix diagonal is inverted using a computationally efficient version of the MIL that takes into account the symmetrical structure of the mentioned submatrices relatively their main diagonals. Computer simulation confirms the performance of the proposed equalizer and demonstrates its efficiency comparing to the unsimplified equalizer. The demo includes the graphs of the equalizer steady-state amplitude-frequency response, the acoustic channel amplitude-frequency responses before and after the equalization, and the power spectral density plots of the equalizer input signal and the signals passed through the equalizer and the acoustic medium. The equalizer can be used in the equipment for the high-quality voice and music reproduction in the conditions of the limited computing resources for the implementation of the equalizer.