Adaptive System Identification in the Short-Time Fourier Transform Domain Using Cross-Multiplicative Transfer Function Approximation

• Published in: IEEE transactions on audio, speech, and language processing Vol. 16; no. 1; pp. 162 - 173
• Main Authors: Avargel, Y., Cohen, I.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.01.2008; Institute of Electrical and Electronics Engineers
• Subjects: Adaptive systems; Algorithms; Applied sciences; Approximation; Convergence; Detection, estimation, filtering, equalization, prediction; Estimating; Exact sciences and technology; Fourier transforms; Function approximation; Information, signal and communications theory; Linear approximation; Linear systems; Mathematical analysis; Miscellaneous; Multiplicative transfer function (MTF); Noise level; Noise levels; short-time Fourier transform (STFT); Signal and communications theory; Signal processing; Signal, noise; Steady-state; subband adaptive filtering; System identification; Telecommunications and information theory; Transfer functions; Performance evaluation; Fourier transformation; Multiplicative transfer function (MTF); Adaptive system; Unsteady state; Function approximation; Modeling; Adaptive method; Implementation; Mean square error; Noise level; short-time Fourier transform (STFT); Acoustic noise; Modulation transfer function; System identification; Transfer function; subband adaptive filtering; Subband decomposition; Acoustic signal processing; Echo suppression; Algorithm; Steady state; Time domain method; Linear system; Signal processing
• ISSN: 1558-7916
• DOI: 10.1109/TASL.2007.910789

In this paper, we introduce cross-multiplicative transfer function (CMTF) approximation for modeling linear systems in the short-time Fourier transform (STFT) domain. We assume that the transfer function can be represented by cross-multiplicative terms between distinct subbands. We investigate the influence of cross-terms on a system identifier implemented in the STFT domain and derive analytical relations between the noise level, data length, and number of cross-multiplicative terms, which are useful for system identification. As more data becomes available or as the noise level decreases, additional cross-terms should be considered and estimated to attain the minimal mean-square error (mse). A substantial improvement in performance is then achieved over the conventional multiplicative transfer function (MTF) approximation. Furthermore, we derive explicit expressions for the transient and steady-state mse performances obtained by adaptively estimating the cross-terms. As more cross-terms are estimated, a lower steady-state mse is achieved, but the algorithm then suffers from slower convergence. Experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach as applied to acoustic echo cancellation.