Journal
IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING
Volume 29, Issue -, Pages 3144-3157Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TASLP.2021.3120650
Keywords
MIMO communication; Frequency-domain analysis; Finite impulse response filters; Adaptive filters; Transfer functions; Matrix decomposition; Matrices; Equalization; inverse filter; multi-channel systems; MIMO systems
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This paper presents a superfast Toeplitz matrix inversion method using FFT techniques, which transforms the non-periodic Toeplitz matrix solution into a periodic framework and utilizes the Woodbury matrix inverse identity. By avoiding the calculation of a large matrix inverse, the method achieves typical computation times and accuracy for equalizing simulated and measured room impulse responses in both single- and multi-channel cases.
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.
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