Note on the use of the Wigner distribution for time-frequency signal analysis

We show that a correct use of the Wigner Distribution (WD) for time-frequency signal analysis requires use of the analytic signal. This version, often referred to as the Wigner-Ville Distribution (WVD), is straightforward to compute, does not exhibit any aliasing problem, and introduces no frequency artifacts. The problems introduced by the use of the Wigner Distribution with a real signal are clarified

Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition

In this paper, the adaptive chirplet decomposition combined with the Wigner-Ville transform and the empirical mode decomposition combined with the Hilbert transform are employed to process various non-stationary signals (strong ground motions and structural responses). The efficacy of these two adaptive techniques for capturing the temporal evolution of the frequency content of specific seismic signals is assessed. In this respect, two near-field and two far-field seismic accelerograms are analyzed. Further, a similar analysis is performed for records pertaining to the response of a 20-story steel frame benchmark building excited by one of the four accelerograms scaled by appropriate factors to simulate undamaged and severely damaged conditions for the structure. It is shown that the derived joint time–frequency representations of the response time histories capture quite effectively the influence of non-linearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event; in this context, tracing the mean instantaneous frequency of records of critical structural responses is adopted. The study suggests, overall, that the aforementioned techniques are quite viable tools for detecting and monitoring damage to constructed facilities exposed to seismic excitations

A Nonstationary Model of Newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and non-stationary nature. The model consists of background and seizure sub-models. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models has a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively)

Proofs for Discrete Time-Frequency Distribution Properties

This technical report contains proofs for a set of mathematical properties of a recently proposed discrete time-frequency distribution class

Accurate and efficient implementation of the time-frequency matched filter

The discrete time--frequency matched filter should replicate the continuous time--frequency matched filter. But the methods differ. To avoid aliasing the discrete method transforms the real-valued signal to the complex-valued analytic signal. The theory for the time--frequency matched filter does not consider the discrete case using the analytic signal. We find that the performance of the matched filter degrades when using the analytic, rather than real-valued, signal. This performance degradation is dependent on the signal to noise ratio and the signal type. In addition, we present a simple algorithm to efficiently compute the time--frequency matched filter. The algorithm with the real-valued signal, comparative to using the analytic signal, requires one-quarter of the computational load. Hence the real-valued signal---and not the analytic signal---enables an accurate and efficient implementation of the time--frequency matched filter

Aircraft flight parameter estimation based on passive acoustic techniques using the polynomial Wigner-Ville distribution

The acoustic signal from an overflying aircraft, as heard by a stationary observer, is used to estimate an aircraft’s constant height, ground speed, range, and acoustic frequency. Central to the success of this flight parameter estimation scheme is the need for an accurate estimate of the instantaneous frequency of the observed acoustic signal. In this paper, the polynomial Wigner–Ville distribution is used in this application as the instantaneous frequency estimator. Its performance and the issue of the optimal time domain window length are addressed

A New Discrete Analytic Signal for Reducing Aliasing in the Discrete Wigner-Ville Distribution

It is not possible to generate an alias-free discrete Wigner--Ville distribution (DWVD) from a discrete analytic signal. This is because the discrete analytic signal must satisfy two mutually exclusive constraints. We present, in this article, a new discrete analytic signal that improves on the commonly used discrete analytic signal's approximation of these two constraints. Our analysis shows that---relative to the commonly used signal---the proposed signal reduces aliasing in the DWVD by approximately 50%. Furthermore, the proposed signal has a simple implementation and satisfies two important properties, namely, that its real component is equal to the original real signal and that its real and imaginary components are orthogonal

An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR

A method for components instantaneous frequency (IF) estimation of multicomponent signals in low signal-to-noise ratio (SNR) is proposed. The method combines a new proposed modification of a blind source separation (BSS) algorithm for components separation, with the improved adaptive IF estimation procedure based on the modified sliding pairwise intersection of confidence intervals (ICI) rule. The obtained results are compared to the multicomponent signal ICI-based IF estimation method for various window types and SNRs, showing the estimation accuracy improvement in terms of the mean squared error (MSE) by up to 23%. Furthermore, the highest improvement is achieved for low SNRs values, when many of the existing methods fail.Scopu

A computationally efficient implementation of quadratic time-frequency distributions

Time-frequency distributions (TFDs) are computationally intensive methods. A very common class of TFDs, namely quadratic TFDs, is obtained by time-frequency (TF) smoothing the Wigner Ville distribution (WVD). In this paper a computationally efficient implementation of this class of TFDs is presented. In order to avoid artifacts caused by circular convolution, linear convolution is applied in both the time and frequency directions. Four different kernel types are identified and separate optimised implementations are presented for each kernel type. The computational complexity is presented for the different kernel types

Foreword to WOSSPA2013 Proceedings

This paper conveys the message presented at the opening ceremony of wosspa2013 in Zeralda, Algeri