Adaptive System Identification in the Short-Time Fourier Transform Domain Using Cross-Multiplicative Transfer Function Approximation
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 i...
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| Published in | IEEE transactions on audio, speech, and language processing Vol. 16; no. 1; pp. 162 - 173 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Piscataway, NJ
IEEE
01.01.2008
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1558-7916 |
| DOI | 10.1109/TASL.2007.910789 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Avargel, Y. Cohen, I. |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Adaptive System Identification in the Short-Time Fourier Transform Domain Using Cross-Multiplicative Transfer Function Approximation |
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