Optimal Detection Using Bilinear Time Frequency and Time Scale Representations
Sayeed, Akbar M.
Jones, Douglas L.
quadratic signal representations; time-frequency representations; time-scale representations
Bilinear time-frequency representations (TFRs) and time-scale representations (TSRs) are potentially very useful for detecting a nonstationary signal in the presence of nonstationary noise or interference. As quadratic signal representations, they are promising for situations in which the optimal detector is a quadratic function of the observations. All existing time-frequency formulations of quadratic detection either implement classical optimal detectors equivalently in the time-frequency domain, without fully exploiting the structure of the TFR, or attempt to exploit the nonstationary structure of the signal in an <i>ad hoc</i> manner. We identify several important nonstationary composite hypothesis testing scenarios for which TFR/TSR-based detectors provide a "natural" framework; that is, in which TFR/TSR-based detectors are both optimal and exploit the many degrees of freedom available in the TFR/TSR. We also derive explicit expressions for the corresponding optimal TFR/TSR kernels. As practical examples, we show that the proposed TFR/TSR detectors are directly applicable to many important radar/sonar detection problems. Finally, we also derive optimal TFR/TSR-based detectors which exploit only partial information available about the nonstationary structure of the signal.
MetadataShow full item record
Showing items related by title, author, creator and subject.
Wavelet-based excitation representation and response determination of linear and nonlinear systems Tratskas, Petros (2002)The dissertation determines the evolutionary spectrum of non-stationary stochastic processes and describes the time-varying characteristics of the response of linear and nonlinear dynamic systems subject to non-stationary ...
Herrera, John Philip (1991)This thesis examines ways in which the re-presentation of the city in literature can serve as a model for the re-presentation of the city in architecture. The vehicle for this investigation is the memory theater, a theater ...