Comparison of techniques for estimating the frequency selectivity of bandlimited channels

A transmission channel used in application such as telecommunications can be modeled as a bandpass filter. Measurement of the frequency selectivity of the channel is important to ensure that the information-bearing signal has minimal distortion and loss of information. A comparison is made for several methods used for estimating the frequency selectivity of the transmission. The methods presented are the correlation method, instantaneous energy and frequency estimation and the cross Wigner-Ville distribution. The theoretical foundations and assumptions are described for each method. In general, all the methods gave similar performance in terms of the frequency selectivity. Due to the shorter analysis duration, both the instantaneous energy and frequency estimation and cross Wigner-Ville distribution is ideal for estimating the frequency selectivity of time-varying channel

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

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

Robust Gravitational Wave Burst Detection and Source Localization in a Network of Interferometers Using Cross Wigner Spectra

We discuss a fast cross-Wigner transform based technique for detecting gravitational wave bursts, and estimating the direction of arrival, using a network of (three) non co-located interferometric detectors. The performances of the detector as a function of signal strength and source location, and the accuracy of the direction of arrival estimation are investigated by numerical simulations.Comment: accepted in Class. Quantum Gravit

Higher-Order Properties of Analytic Wavelets

The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a two-parameter family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a mapping between scale and frequency, and the bias involved in estimating properties of modulated oscillatory signals, are proposed as important considerations. Wavelet behavior is found to be strongly impacted by the degree of asymmetry of the wavelet in both the frequency and the time domain, as quantified by the third central moments. A particular subset of the generalized Morse wavelets, recognized as deriving from an inhomogeneous Airy function, emerge as having particularly desirable properties. These "Airy wavelets" substantially outperform the only approximately analytic Morlet wavelets for high time localization. Special cases of the generalized Morse wavelets are examined, revealing a broad range of behaviors which can be matched to the characteristics of a signal.Comment: 15 pages, 6 Postscript figure

Time-frequency detection of Gravitational Waves

We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and signal components. The noise component approximates initial LIGO interferometer noise. The signal components have the time and frequency characteristics postulated by Flanagan and Hughes for binary black hole coalescence. The signals correspond to binaries with total masses between $45 M_\odot$ to $70 M_\odot$ and with (optimal filter) signal-to-noise ratios of 7 to 12. The method is implementable in real time, and achieves a coincident false alarm rate for two detectors $\approx$ 1 per 475 years. At this false alarm rate, the single detector false dismissal rate for our signal model is as low as 5.3% at an SNR of 10. We expect to obtain similar or better detection rates with this method for any signal of similar power that satisfies certain adiabaticity criteria. Because optimal filtering requires knowledge of the signal waveform to high precision, we argue that this method is likely to detect signals that are undetectable by optimal filtering, which is at present the best developed detection method for transient sources of gravitational waves.Comment: 24 pages, 5 figures, uses REVTE