Samir Ouelha

Designing high-resolution time–frequency and time–scale distributions for the analysis and classification of non-stationary signals: a tutorial review with a comparison of features performance

This paper deals with the problem of extracting information from non-stationary signals in the form of features that can be used for effective decision-making in both data analysis and machine learning for automatic classification systems. Suitable time–frequency (TF) and time–scale (TS) representations of such signals are reviewed for these purposes, and, the relationships between such TF and TS signal transformations is discussed. Both linear (atomic) decompositions and quadratic distributions are considered as well as other related methods such as fractional Fourier transform, polynomial Wigner–Ville distributions and time-varying order spectra. Current state-of-the-art methods are reviewed, and new results are presented including extensions of existing methods. Machine learning methodologies using TF/TS features can result in the design of systems that improve the classification of non-stationary signals. Using selected TF distributions (TFDs) and TS distributions (TSDs), the extraction of such TF/TS features is demonstrated on multi-channel recordings using channel fusion or feature fusion approaches. Extending the findings of previous studies, a TF/TS feature set is formed by including two complementary categories: signal related features and image features. The design of high-resolution TF/TS algorithms is then refined to account for issues of accuracy and robustness. Then, the desired TF/TS features are selected using different feature selection algorithms and compared with respect to the classification performance. Finally, other features from related methods are added, and comparisons performed. Improvements of up to 5% are obtained when using the chosen feature set after wrapper feature selection with channel feature fusion.

An efficient inverse short-time Fourier transform algorithm for improved signal reconstruction by time-frequency synthesis

This paper presents an improved signal reconstruction method based on a new inverse short-time Fourier transform (ISTFT) estimator. The main challenge addressed in this study is to design a more computationally efficient algorithm called exact formal approach (EFA) which overcomes the drawbacks of the popular overlap and add (OLA) and least squares (LS) methods in several cases of practical interest. The proposed EFA algorithm is based on a vector formulation and the exploitation of properties of the matrix formed by signal samples and frames corresponding to signals segments with overlap. A detailed comparative study shows the advantages of the EFA compared to the OLA and LS methods. Several experiments illustrate the performance and properties of the different estimators. The criteria of comparison are based on synthesis quality and denoising efficiency. The results indicate that, (1) from a computational point of view, the proposed algorithm EFA outperforms other popular ISTFT algorithms including OLA and LS and (2) that the EFA and LS have similar results in terms of synthesis quality and both outperform the algorithm currently most used for ISTFT, the OLA. The proposed EFA estimator can then improve ISTFT based applications involving signal enhancement and denoising.

Improving DOA Estimation Algorithms Using High-Resolution Quadratic Time-Frequency Distributions

This paper addresses the problem of direction of arrival (DOA) estimation and blind source separation (BSS) for nonstationary signals in the underdetermined case. These two problems are strongly related to the mixing matrix estimation problem. To deal with the nonstationary characteristics of signals, this study uses high-resolution quadratic time-frequency distributions (TFDs) to reduce cross-terms while keeping a good resolution for the construction of spatial TFDs. The main contributions of this paper are two-fold. First, the formulation of a statistical test for the noise thresholding step improves robustness and avoids the use of empirical parameters; this test performs multisource selection of the time-frequency points where the signal of interest is present. Second, an algorithm based on image processing methods performs an auto-source selection for mixing matrix estimation. The results on simulated signals demonstrate an improvement of 10 dB in terms of normalized mean square error for BSS and 7% in terms of relative error for DOA estimation over standard methods.

A robust high-resolution time–frequency representation based on the local optimization of the short-time fractional Fourier transform

The Locally Optimized Spectrogram (LOS) defines a novel method for obtaining a high-resolution time-frequency (t, f) representation based on the short-time fractional Fourier transform (STFrFT). The key novelty of the LOS is that it automatically determines the locally optimal window parameters and fractional order (angle) for all signal components, leading to a high-resolution and cross-terms free time frequency representation. This method is suitable for multicomponent and non-stationary signals without a priori signal information. Simulated signals, real biomedical applications, and various measures are used to validate the improved performance of the LOS and compare it with other state-of-the-art methods. The robustness of the LOS is also demonstrated under different signal-to-noise ratio (SNR) conditions. Finally, the relationship between the LOS and other time-frequency distributions (TFDs) is depicted and a recursive formulation is presented and shows the trade-off between the cross-terms suppression and auto-terms resolution

Performance evaluation of time-frequency image feature sets for improved classification and analysis of non-stationary signals: Application to newborn EEG seizure detection

Abstract This study demonstrates that a time-frequency (TF) image pattern recognition approach offers significant advantages over standard signal classification methods that use t-domain only or f-domain only features. Two approaches are considered and compared. The paper describes the significance of the standard TF approach for non-stationary signals; TF signal (TFS) features are defined by extending t-domain or f-domain features to a joint (t, f) domain resulting in e.g. TF flatness and TF flux. The performance of the extended TFS features is comparatively assessed using Receiver Operating Characteristic (ROC) analysis Area Under the Curve (AUC) measure. Experimental results confirm that the extended TFS features generally yield improved performance (up to 19%) when compared to the corresponding t-domain and f-domain features. The study also explores a second approach based on novel TF image (TFI) features that further improves TF-based classification of non-stationary signals. New TFI features are defined and extracted from the (t, f) domain; they include TF Hu invariant moments, TF Haralick features, and TF Local Binary Patterns (LBP). Using a state-of-the-art classifier, different metrics based on confusion matrix performance are compared for all extended TFS features and TFI features. Experimental results show the improved performance of TFI features over both TFS features and t-domain only or f-domain only features, for all TF representations and for all the considered performance metrics. The experiment is validated by comparing this new proposed methodology with a recent study, utilizing the same large and complex data set of EEG signals, and the same experimental setup. The resulting classification results confirm the superior performance of the proposed TFI features with accuracy improvement up to 5.52%.

An improved time–frequency noise reduction method using a psycho-acoustic Mel model

This paper addresses the problem of noise reduction in non-stationary signals. The paper first describes a human physiology based time–frequency (TF) representation (HPTF) using Mel filterbanks. It is then used to improve a noise reduction algorithm that does not require any a priori information about the signal of interest and the noise. This algorithm is efficiently implemented using an original wavelet shrinkage method. The overall method results in an original TF denoising procedure that yields a denoised HPTF (DHPTF). From this representation, one can reconstruct a denoised time-domain signal and therefore define a new improved noise reduction algorithm, whose performance is evaluated and compared with other state-of-the-art methods. The performance assessment uses several criteria: (1) signal-to-noise-ratio (SNR), (2) segmental SNR (SSNR) and (3) mean square error (MSE). The results indicate an improvement of up to 4.72 dB with respect to (w.r.t.) SNR, 2.79 dB w.r.t. SSNR and 4.72 dB w.r.t. MSE for a speech database signals corrupted with four different noises. In addition, other applications such as EEG signal enhancement show promising results.

Refining the ambiguity domain characteristics of non-stationary signals for improved time–frequency analysis: Test case of multidirectional and multicomponent piecewise LFM and HFM signals

Abstract This paper aims at providing a more accurate description of the ambiguity domain characteristics of a piecewise multicomponent non-stationary signals with focus on piece-wise linear frequency modulated (LFM) (PW-LFM) signal and a mixed LFM and hyperbolic FM (HFM). The main motivation comes from the observed PW-LFM nature of several real life signals. It is essential that the characteristics of these types of signals be taken into account for the design of high resolution Time–Frequency Distributions (TFDs) and therefore to improve the application and interpretation of time–frequency signal analysis and processing. In this paper the ambiguity function (AF) of a general PW-LFM signal is derived exactly and then analyzed to deduce important properties. The precise location and behavior of both auto-terms and cross-terms of a general piecewise LFM signal can be deduced from its AF. Numerical simulations using different types of test signals confirm the analytical derivations. An extension of the PW-LFM test signal is also presented by using HFM signals. For such signals, the exact analytical expression of auto-terms is given as well as the expression of cross-terms between HFM and LFM. The results obtained can be used in future studies to design more advanced quadratic time–frequency distributions (QTFDs) that exhibit improved properties in terms of resolution and accuracy.