Time-frequency Functions Research Articles

Wave physics of the frequency difference autoproduct: Bilinear time-frequency analysis

Frequency difference beamforming (Abadi et al., 2012, JASA, 132, 3018-3029) and matched field processing (Worthmann et al., 2015, JASA, 138, 3549-3562) are array signal processing techniques that determine acoustic ray-path directions and source locations, respectively, from sparse array recordings by shifting the signal processing to a lower, out-of-band, difference-frequency bandwidth. This frequency down-shift is accomplished through the use of the frequency difference autoproduct (Δf-AP), a quadratic product of complex frequency-domain acoustic field amplitudes at two different frequencies. In this presentation, the physical and mathematical underpinnings of this quadratic product are discussed. Specifically, in the branch of applied mathematics termed bilinear time-frequency analysis, this Δf-AP is actually one of four quadratic time-frequency functions, each inter-related through forward and inverse Fourier transforms. The other three functions are the time-domain autoproduct, the Wigner distribution, and the ambiguity function. These four functions and several of their interesting properties are reviewed, including their relationship to the Wiener-Khintchine Theorem, and the spatial and spectral coherence and correlation functions. Additionally, the behavior of these functions when evaluated from simulated acoustic recordings from ideal single-path and multi-path acoustic environments is shown and compared. [Sponsored by ONR and NSF.]

Parametric Time-Frequency Analysis and Its Applications in Music Classification

Analysis of nonstationary signals, such as music signals, is a challenging task. The purpose of this study is to explore an efficient and powerful technique to analyze and classify music signals in higher frequency range (44.1 kHz). The pursuit methods are good tools for this purpose, but they aimed at representing the signals rather than classifying them as in Y. Paragakin et al., 2009. Among the pursuit methods, matching pursuit (MP), an adaptive true nonstationary time-frequency signal analysis tool, is applied for music classification. First, MP decomposes the sample signals into time-frequency functions or atoms. Atom parameters are then analyzed and manipulated, and discriminant features are extracted from atom parameters. Besides the parameters obtained using MP, an additional feature, central energy, is also derived. Linear discriminant analysis and the leave-one-out method are used to evaluate the classification accuracy rate for different feature sets. The study is one of the very few works that analyze atoms statistically and extract discriminant features directly from the parameters. From our experiments, it is evident that the MP algorithm with the Gabor dictionary decomposes nonstationary signals, such as music signals, into atoms in which the parameters contain strong discriminant information sufficient for accurate and efficient signal classifications.

Application of Hilbert-Huang Transform Method for Analyzing Toxic Concentrations in the Niagara River

A novel application of the Hilbert-Huang transform (HHT) method for the analysis of nonstationary and nonlinear time series is proposed in this paper. The HHT is introduced to the field of water quality analysis both to evaluate trends and to assess the cause-effects relationship between the system under study and external physical factors. The HHT combines two distinct analytical methods: the empirical mode decomposition (EMD) to decompose observed series into independent intrinsic mode functions and the Hilbert transform to transform these time-dependent functions into time-frequency functions. A practical application of the HHT method for data analysis is presented herein for four time series in the Niagara River: flow, water temperature, and incoming concentrations of two polycyclic aromatic hydrocarbons. It is shown that the EMD improves the spectral representation of the original time series, enabling a better detection of periodic trends and dominant time scales. It is concluded that the ability of...

Occipital EEG correlates of conscious awareness when subjective target shine-through and effective visual masking are compared: Bifocal early increase in gamma power and speed-up of P1

Neural correlates of conscious awareness can be comfortably studied when awareness of the target stimuli is a varying dependent variable in the experimental conditions where the key independent variables are kept invariant. We presented vernier targets backward masked by an invariant grating with invariant SOA. EEG data recorded from occipital and parietal electrodes was analyzed for ERPs and time-frequency functions of oscillatory responses. Comparison of data from correct aware trials with data from correct unaware trials showed that conscious awareness of targets was associated with decrease in the latency of ERP/P1, increase in the amplitude of P300, and increase in the power of 70-Hz and 30-Hz gamma band oscillations from 50 ms before target onset up to 100 ms after target onset. Results are interpreted in the context of the well-known views about the role of brain-activity oscillations in conscious awareness and as related to the perceptual retouch theory.

Spectral decomposition using Wigner-Ville distribution with applications to carbonate reservoir characterization

Spectral decomposition of seismic data transforms seismic amplitudes as a function of space and time into spectral amplitudes as a function of frequency, space, and time. It has been used for a variety of applications including determination of layer thickness, stratigraphic visualization, reservoir characterization, and direct hydrocarbon detection. The commonly used spectral decomposition methods—such as STFT (short-time Fourier transform), CWT (continuous wavelet transform), and MPD (matching pursuit decomposition)—are linear in that they compute correlations between the signal and a family of time-frequency functions. Thus, they cannot achieve arbitrarily fine resolution in the time and frequency domain simultaneously due to the limitations imposed by the uncertainty principle (Qian, 2005).

Interference Excision in Spread Spectrum Communications Using Adaptive Positive Time-Frequency Analysis

This paper introduces a novel algorithm to excise single and multicomponent chirp-like interferences in direct sequence spread spectrum (DSSS) communications. The excision algorithm consists of two stages: adaptive signal decomposition stage and directional element detection stage based on the Hough-Radon transform (HRT). Initially, the received spread spectrum signal is decomposed into its time-frequency (TF) functions using an adaptive signal decomposition algorithm, and the resulting TF functions are mapped onto the TF plane. We then use a line detection algorithm based on the HRT that operates on the image of the TF plane and detects energy varying directional elements that satisfy a parametric constraint. Interference is modeled by reconstructing the corresponding TF functions detected by the HRT, and subtracted from the received signal. The proposed technique has two main advantages: (i) it localizes the interferences on the TF plane with no cross-terms, thus facilitating simple filtering techniques based on thresholding of the TF functions, and is an efficient way to excise the interference; (ii) it can be used for the detection of any directional interferences that can be parameterized. Simulation results with synthetic models have shown successful performance with linear and quadratic chirp interferences for single and multicomponent interference cases. The proposed method excises the interference even under very low SNR conditions of dB, and the technique could be easily extended to any interferences that could be represented by a parametric equation in the TF plane.

A mixing model for separate feedstream chemical reactors and its optimum performance

A mixing model for separate feedstream reactors which can be used to represent continuous flow systems with variable mixing and variable rate of reactant addition along the flow direction is proposed. The residence time frequency functions are presented. Representation of the additional degrees of freedom by a continuous progression allows optimum parameter values to be obtained by direct search algorithms. Results obtained using the complex algorithm of Box correlate the optimum operating policies for one particular set of parallel reactions.

A mixing model for separate feedstream chemical reactors and its optimum performance

A mixing model for separate feedstream reactors which can be used to represent continuous flow systems with variable mixing and variable rate of reactant addition along the flow direction is proposed. The residence time frequency functions are presented. Representation of the additional degrees of freedom by a continuous progression allows optimum parameter values to be obtained by direct search algorithms. Results obtained using the complex algorithm of Box correlate the optimum operating policies for one particular set of parallel reactions.