Gordon J. Frazer

Time-varying higher-order spectra, generalised Wigner-Ville distribution and the analysis of underwater acoustic data

The Wigner-Ville distribution (WVD) is a second-order time-frequency representation in the sense that it is able to give ideal energy concentration for quadratic phase FM signals, and its expectation value is a second order time-varying spectrum. The generalized WVD (GWVD) is defined by extension so as to achieve ideal energy concentration for higher order phase laws. In addition, by taking the expected value of the GWVD, time-varying higher-order spectra can be defined. The merit of including time-varying higher-order spectral information when analyzing underwater acoustic signals is demonstrated.<<ETX>>

A wideband, synthetic aperture beamformer for through-the-wall imaging

A coarray-based aperture synthesis scheme using subarrays and post-data acquisition beamforming is presented for through-the-wall wideband microwave imaging applications. Various effects of the presence of the wall, such as refraction, change in speed, and attenuation, are incorporated into the beamformer design. Simulation results verifying the proposed synthetic aperture technique for a TWI system are presented. The effects of incorrect estimates of the parameters of the wall, such as thickness and dielectric constant, on performance are investigated.

Spatial Time-Frequency Distributions: Theory and Applications

This chapter presents a comprehensive treatment of the hybrid area of time-frequency distributions (TFDs) and array signal processing. The application of quadratic ‘l’F’Ds to sensor signal processing has recently become of interest, and it was necessitated by the need to address important problems related to processing nonstationary signals incident on multiantenna receivers. Over the past few years, major contributions have been made to improve direction finding and blind source separation using time-frequency signatures. This improvement has cast quadratic TFDs as a key tool for source localization and signal recovery, and put bilinear transforms at equal footing with second-order and higher-order statistics as bases for effective spatial-temporal signal processing. This chapter discusses the advances made through time-frequency analysis in direction-of-arrival estimation, signal synthesis, and near-field source characterization.

Concurrent Operation of Two Over-the-Horizon Radars

By exploiting the reflective and refractive nature of high-frequency (HF) radiowave propagation through the ionosphere or the conducting sea surface, over-the-horizon radar (OTHR) systems perform wide-area surveillance at long range well beyond the limit of the horizon of conventional line-of-sight (LOS) radars. Improved characterizations of the targets can be achieved by using multiple OTHRs operating simultaneously as compared to a single OTHR operating alone. In this paper, we consider concurrent operations of two OTHR systems that occupy the same frequency band with different chirp waveforms. The objective is to respond to the advanced wide-area surveillance needs without reducing the wave repetitive frequency. For this purpose, a new cross-radar interference cancellation technique is developed and its effectiveness is verified through both analytical and simulation results

Wigner bispectrum, phase product smoothing and time-varying bispectra

Time-varying higher order spectra (TVHOS) based analysis is an emerging technique for analyzing signals which are non-stationary, non-Gaussian and nonlinear. Most TVHOS are derived from the Wigner-Ville distribution (WVD), and in particular, retain the lag centering property of the WVD. When extended to third and higher orders, calculation of TVHOS can be complicated by the need for signal interpolation, imposed by the requirement for lag centering. The authors derive a phase product relationship which allows the lag centred Wigner bispectrum to be computed in a simpler way using a non-lag centered time-varying bispectrum. For smoothed Wigner bispectra, the phase product term can be included in the smoothing function and so requires no additional computation. This result is demonstrated for the second-order case, where the WVD is computed using a non-lag centered Rihaczek time-frequency distribution.<<ETX>>

The bispectral aliasing test

Digital signal processing of continuous signals requires sampling of the continuous signal. When sampling continuous signals it is important to avoid the effect called aliasing. Aliasing causes signals at particular frequencies to appear, erroneously, as signals of different frequencies. Consequently, it is important that before any digital signal processing is performed, the sampled signal is known to be free of aliasing. A published test based on the bispectrum purports to be able to detect aliasing of an already sampled signal. The authors provide counter examples to demonstrate that this previously published test for aliasing is not valid in practice.<<ETX>>

A new approach for near-field wideband synthetic aperture beamforming

A coarray-based synthetic aperture beamformer using stepped-frequency signal synthesis and post-data acquisition processing is presented for wideband imaging of near-field scenes. The proposed beamformer formulation and implementation finds key applications in through-the-wall microwave imaging and landmine detection problems. While coarray techniques offer significant reduction in array elements for a given angular resolution, stepped-frequency realization of wideband systems simplifies implementation and offers flexibility in beamforming. Proof of concept is provided using real data collected in an anechoic chamber.

Detection of underwater transient acoustic signals using time-frequency distributions and higher-order spectra

The authors demonstrate the application of the Wigner-Ville time-frequency distribution, the bispectrum, the time-varying bispectrum, and Gerrs third-order Wigner distribution to some underwater acoustic data. They also demonstrate the merit of including higher-order spectral information when signaturing underwater acoustic sources. It is pointed out that conventional signal analysis procedures do not utilize all the information available in many practical signal analysis problems. It is shown that the use of higher-order spectral analysis improves time, frequency, and time-frequency analysis methods and provides the analyst with important additional information. Time-varying higher-order spectra are not well developed and are difficult to interpret. Phase coupling cannot be detected without some form of ensemble averaging. This important feature of the stationary bispectrum, where for single signal realization problems ensemble averages are often replaced by temporal averages, does not carry through to time-varying higher-order spectra.<<ETX>>

Multiple view time-frequency distributions

We propose a new approach for constructing time-frequency distributions and spectra which achieves improved localisation in the time-frequency plane while retaining the non-negativity property of an energy distribution. The approach is to construct a composite distribution from multiple views of the Wigner-Ville distribution. Each view is obtained by smoothing the WVD with an asymmetric Gaussian kernel of sufficient time-bandwidth product to ensure non-negativity. Different views are generated by rotating the orientation of the Gaussian kernel in the time-frequency plane. Within the general multiple view framework we state and demonstrate one ad-hoc procedure for combining the views and suggest a second.<<ETX>>

Time-frequency analysis for maneuvering target detection in over-the-horizon radars

A novel linear time-frequency representation method is proposed for source detection and classification in over-the-horizon radar (OTHR) systems. Of particular interest is the estimation and identification of the multipaths of maneuvering targets described as multicomponent time-Doppler signatures in the presence of strong clutter. By approximating the time-Doppler signatures as chirp signals in each block of time period, chirp signal analysis is used to estimate the chirp parameters (chirp rates and center frequencies) of the clutter and target signal components. Clutter components, which are localized around the low chirp rates and frequencies, are effectively suppressed through subspace projections. The target signals are then dechirped, which is followed by either conventional DFT transform or high-resolution spectrum estimation methods for center frequency estimation.