Ph.D Thesis | |

Ph.D Student | Avargel Yekutiel |
---|---|

Subject | System Identification in the Short-Time Fourier Transform Domain |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROF. Israel Cohen |

Full Thesis text |

The dissertation addresses theory and applications of linear and nonlinear system identification in the short-time Fourier transform (STFT) domain. It is well known that in order to perfectly represent a linear system in the STFT domain, crossband filters between subbands are generally required. Practically, however, the estimation of these filters is avoided, as it was shown to worsen the system estimate accuracy.

In this thesis, we investigate the
problems of *model-structure selection* and *model-order selection*
for system identification in the STFT domain. We start by investigating the influence
of undermodeling caused by restricting the number of estimated crossband
filters on the system identification performance. We analytically show that
increasing the number of crossband filters not necessarily implies a lower
mean-square error (mse) in subbands. We show that as the signal-to-noise ratio
(SNR) increases or as more data is employable, the optimal model complexity
increases, and correspondingly additional crossband filters can be estimated to
achieve better estimation accuracy. This strategy of controlling the number of
crossband filters is successfully applied to acoustic echo cancellation
applications in batch or adaptive forms.

We proceed with the widely-used multiplicative transfer function (MTF) approximation, which avoids the crossband filters by approximating the linear system as multiplicative in the STFT domain. We provide a detailed mean-square analysis and show that the system identification performance does not necessarily improve by increasing the length of the analysis window. The optimal window length, that achieves the minimal mse, depends on the SNR and the data length. These results are used for deriving new models for linear systems in the STFT domain.

The research is then extended to *nonlinear*
system identification, and a novel nonlinear STFT model is introduced for this
purpose. The model consists of a parallel combination of a linear component,
represented by crossband filters between subbands, and a nonlinear component,
which is modeled by multiplicative cross-terms. We mainly concentrate on the
error caused by nonlinear undermodeling; that is, when a purely linear model is
employed for identifying the nonlinear system. We show that for low SNRs, a
lower mse is achieved by allowing for nonlinear undermodeling that utilizes a
purely linear model; whereas as the SNR increases, the performance can be
generally improved by estimating the full nonlinear model. We further show that
a significant reduction in computational cost as well as a substantial
improvement in estimation accuracy can be achieved over the conventional
time-domain Volterra model.