Spatial Time-frequency Distributions Research Articles

Blind Separation of Nonstationary Sources

We propose a blind separation technique for nonstationary sources that exploits both auto-terms and cross-terms of the time-frequency distributions. The technique is based on the simultaneous joint diagonalization and off-diagonalization of spatial time-frequency distributions. Computer simulations demonstrate the superiority of the approach in comparison with other time-frequency based methods.

Two Contributions to Blind Source Separation Using Time–Frequency Distributions

We present two improvements/extensions of a previous deterministic blind source separation (BSS) technique, by Belouchrani and Amin, that involves joint-diagonalization of a set of Cohen's class spatial time-frequency distributions. The first contribution concerns the extension of the BSS technique to the stochastic case using spatial Wigner-Ville spectrum. Then, we show that Belouchrani and Amin's technique can be interpreted as a practical implementation of the general equations we provide in the stochastic case. The second contribution is a new criterion aimed at selecting more efficiently the time-frequency locations where the spatial matrices should be joint-diagonalized, introducing single autoterms selection. Simulation results on stochastic time-varying autoregressive moving average (TVARMA) signals demonstrate the improved efficiency of the method.

Bilinear signal synthesis in array processing

Multiple source signals impinging on an antenna array can be separated by time-frequency synthesis techniques. Averaging of the time-frequency distributions (TFDs) of the data across the array permits the spatial signatures of sources to play a fundamental role in improving the synthesis performance. Array averaging introduces a weighting function in the time-frequency domain that decreases the noise levels, reduces the interactions of the source signals, and mitigates the crossterms. This is achieved independent of the temporal characteristics of the source signals and without causing any smearing of the signal terms. The weighting function may take noninteger values, which are determined by the communication channel, the source positions, and their angular separations. Unlike the recently devised blind source separation methods using spatial TFDs, the proposed method does not require whitening or retrieval of the source directional matrix. The paper evaluates the proposed method in terms of performance and computations relative to the existing source separation techniques based on quadratic TFDs.

Subspace analysis of spatial time-frequency distribution matrices

Spatial time-frequency distributions (STFDs) have been previously introduced as the natural means to deal with source signals that are localizable in the time-frequency domain. Previous work in the area has not provided the eigenanalysis of STFD matrices, which is key to understanding their role in solving direction finding and blind source separation problems in multisensor array receivers. The aim of this paper is to examine the eigenstructure of the STFD matrices. We develop the analysis and statistical properties of the subspace estimates based on STFDs for frequency modulated (FM) sources. It is shown that improved estimates are achieved by constructing the subspaces from the time-frequency signatures of the signal arrivals rather than from the data covariance matrices, which are commonly used in conventional subspace estimation methods. This improvement is evident in a low signal-to-noise ratio (SNR) environment and in the cases of closely spaced sources. The paper considers the MUSIC technique to demonstrate the advantages of STFDs and uses it as grounds for comparison between time-frequency and conventional subspace estimates.

Direction Finding Based on Spatial Time-Frequency Distribution Matrices

Amin, Moeness G., and Zhang, Yimin, Direction Finding Based on Spatial Time-Frequency Distribution Matrices, Digital Signal Processing10 (2000), 325–339.Spatial time-frequency distributions (STFDs) have been recently introduced as the natural means to deal with source signals that are localizable in the time-frequency domain. It has been shown that improved estimates of the signal and noise subspaces are achieved by constructing the subspaces from the time-frequency signatures of the signal arrivals rather than from the data covariance matrices, which are commonly used in conventional subspace estimation methods. This paper discusses the application of STFD to high-resolution direction finding. We focus on both the role and the effect of crossterms in angle estimation when multiple time-frequency points are incorporated. Simulation examples are presented to compare the performance of joint block-diagonalization and time-frequency averaging techniques for incorporating multiple autoterm and crossterm points in subspace estimation.

Wideband direction-of-arrival estimation of multiple chirp signals using spatial time-frequency distributions

The recently developed concept of narrowband spatial time-frequency distributions (STFDs) is extended to the wide-band case. A new STFD-based wideband root-MUSIC estimator is proposed. This technique employs an extended coherent signal-subspace (CSS) principle involving coherent averaging over a pre-selected set of time-frequency points rather than the conventional frequency-only averaging procedure.

Large-scale neocortical dynamics: Some EEG data analysis implications

The spatial time-frequency distribution matrix and associated Rényi entropy is proposed as the basis for a method that may be useful for estimating the significance of nonlocal neocortical interactions in the analysis of scalp EEG data. Implications of nonlocal interactions for source estimation are also considered.

Time-frequency MUSIC

A new method for the estimation of the signal subspace and noise subspace based on time-frequency signal representations is introduced. The proposed approach consists of the joint block-diagonalization (JBD) of a set of spatial time-frequency distribution matrices. Once the signal and noise subspaces are estimated, any subspace based approach, including the multiple signal classification (MUSIC) algorithm, can be applied for direction of arrival (DOA) estimation. Performance of the proposed time-frequency MUSIC (TF-MUSIC) for an impinging chirp signal using three different kernels is numerically evaluated.

On the Use of Spatial Time Frequency Distributions forSignal Extraction

This paper deals with the extraction of signals from their instantaneous linear mixtures using time-frequency distributions. Fundamentally, this problem is a signal synthesis from the time-frequency (t-f) plane. However with the incorporation of the spatial information provided by a multisensor array, the problem can be posed as special case of blind source separation. So far, the blind source separation has been solved using only statistical information available on the source signals. Herein, we propose to solve the aforementioned problem using time-frequency signal representations and the spatial array aperture. The proposed approach relies on the difference in the t-f signatures of the sources to be separated. It is based on the diagonalization of a combined set of spatial time-frequency distribution matrices. A numerical example is provided to illustrate the effectiveness of our method.