This paper gives a survey of frequency domain iden- tification methods for rational transfer functions in the Laplace (s) or z-domain. The interrelations between the different ap- proaches are highlighted through a study of the (equivalent) cost functions. The properties of the various estimators are discussed and illustrated by several examples.

Objective. When a person listens to continuous speech, a corresponding response is elicited in the brain and can be recorded using electroencephalography (EEG). Linear models are presently used to relate the EEG recording to the corresponding speech signal. The ability of linear models to find a mapping between these two signals is used as a measure of neural tracking of speech. Such models are limited as they assume linearity in the EEG-speech relationship, which omits the nonlinear dynamics of the brain. As an alternative, deep learning models have recently been used to relate EEG to continuous speech. Approach. This paper reviews and comments on deep-learning-based studies that relate EEG to continuous speech in single- or multiple-speakers paradigms. We point out recurrent methodological pitfalls and the need for a standard benchmark of model analysis. Main results. We gathered 29 studies. The main methodological issues we found are biased cross-validations, data leakage leading to over-fitted models, or disproportionate data size compared to the model’s complexity. In addition, we address requirements for a standard benchmark model analysis, such as public datasets, common evaluation metrics, and good practices for the match-mismatch task. Significance. We present a review paper summarizing the main deep-learning-based studies that relate EEG to speech while addressing methodological pitfalls and important considerations for this newly expanding field. Our study is particularly relevant given the growing application of deep learning in EEG-speech decoding.

The objective of this paper is threefold: (1) to provide an extensive review of signal subspace speech enhancement, (2) to derive an upper bound for the performance of these techniques, and (3) to present a comprehensive study of the potential of subspace filtering to increase the robustness of automatic speech recognisers against stationary additive noise distortions. Subspace filtering methods are based on the orthogonal decomposition of the noisy speech observation space into a signal subspace and a noise subspace. This decomposition is possible under the assumption of a low-rank model for speech, and on the availability of an estimate of the noise correlation matrix. We present an extensive overview of the available estimators, and derive a theoretical estimator to experimentally assess an upper bound to the performance that can be achieved by any subspace-based method. Automatic speech recognition experiments with noisy data demonstrate that subspace-based speech enhancement can significantly increase the robustness of these systems in additive coloured noise environments. Optimal performance is obtained only if no explicit rank reduction of the noisy Hankel matrix is performed. Although this strategy might increase the level of the residual noise, it reduces the risk of removing essential signal information for the recogniser's back end. Finally, it is also shown that subspace filtering compares favourably to the well-known spectral subtraction technique.

An effective way to increase the noise robustness of automatic speech recognition is to label noisy speech features as either reliable or unreliable (missing), and to replace (impute) the missing ones by clean speech estimates. Conventional imputation techniques employ parametric models and impute the missing features on a frame-by-frame basis. At low signal-to-noise ratios (SNRs), these techniques fail, because too many time frames may contain few, if any, reliable features. In this paper, we introduce a novel non-parametric, exemplar-based method for reconstructing clean speech from noisy observations, based on techniques from the field of Compressive Sensing. The method, dubbed sparse imputation, can impute missing features using larger time windows such as entire words. Using an overcomplete dictionary of clean speech exemplars, the method finds the sparsest combination of exemplars that jointly approximate the reliable features of a noisy utterance. That linear combination of clean speech exemplars is used to replace the missing features. Recognition experiments on noisy isolated digits show that sparse imputation outperforms conventional imputation techniques at SNR = -5 dB when using an ideal `oracle' mask. With error-prone estimated masks sparse imputation performs slightly worse than the best conventional technique.