Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

A windowed graph Fourier transform

Abstract: The prevalence of signals on weighted graphs is increasing; however, because of the irregular structure of weighted graphs, classical signal processing techniques cannot be directly applied to signals on graphs. In this paper, we define generalized translation and modulation operators for signals on graphs, and use these operators to adapt the classical windowed Fourier transform to the graph setting, enabling vertex-frequency analysis. When we apply this transform to a signal with frequency components that vary along a path graph, the resulting spectrogram matches our intuition from classical discrete-time signal processing. Yet, our construction is fully generalized and can be applied to analyze signals on any undirected, connected, weighted graph.

Real-time frequency and 2-D angle estimation with sub-Nyquist spatio-temporal sampling

Abstract: An algorithm is presented for real-time estimation of the frequency and azimuth and elevation angles of each signal incident on an airborne antenna array system over a very wide frequency band (2-18 GHz) commensurate with electronic signal warfare. The algorithm provides unambiguous frequency estimation despite severe temporal undersampling necessitated by cost/complexity of hardware considerations. The 2-18 GHz spectrum is decomposed into 1-GHz bands. The baseband output of each antenna is sent through two 250-MHz sampled channels where one is delayed relative to the other (prior to sampling) by 0.5 ns, which is the Nyquist interval for a 1-GHz bandwidth. Due to the high variance of the Direct ESPRIT frequency estimator, aliased frequencies are estimated via a simple formula and translated to the proper aliasing zone, utilizing eigenvector information generated by PRO-ESPRIT. The algorithm also provides unambigous 2-D angle estimate over the entire 2-18 GHz bandwidth, despite severe spatial undersampling at the higher end of this band necessitated by mutual coupling considerations and resolving power requirements at the lower end of the band. Eigenvector information generated by PRO-ESPRTT is used to facilitate computationally simple estimation of azimuth and elevation angles that are automatically paired with corresponding frequency estimates despite aliasing. Simulations are presented demonstrating the capabilities of the algorithm. >

Epileptic Seizure Classification of EEGs Using Time–Frequency Analysis Based Multiscale Radial Basis Functions

Abstract: The automatic detection of epileptic seizures from electroencephalography (EEG) signals is crucial for the localization and classification of epileptic seizure activity. However, seizure processes are typically dynamic and nonstationary, and thus, distinguishing rhythmic discharges from nonstationary processes is one of the challenging problems. In this paper, an adaptive and localized time–frequency representation in EEG signals is proposed by means of multiscale radial basis functions (MRBF) and a modified particle swarm optimization (MPSO) to improve both time and frequency resolution simultaneously, which is a novel MRBF-MPSO framework of the time–frequency feature extraction for epileptic EEG signals. The dimensionality of extracted features can be greatly reduced by the principle component analysis algorithm before the most discriminative features selected are fed into a support vector machine (SVM) classifier with the radial basis function (RBF) in order to separate epileptic seizure from seizure-free EEG signals. The classification performance of the proposed method has been evaluated by using several state-of-art feature extraction algorithms and other five different classifiers like linear discriminant analysis, and logistic regression. The experimental results indicate that the proposed MRBF-MPSO-SVM classification method outperforms competing techniques in terms of classification accuracy, and shows the effectiveness of the proposed method for classification of seizure epochs and seizure-free epochs.