Engineering topics
Publications and source records attributed to Van Trees, H. L..
Book on nonlinear modulation based on optimum estimation theory covering phase synchronization, analog data transmission, digital and analog systems performance, Markov processes, etc
Book on detection, estimation and modulation theory, Part 3, Gaussian and radar-sonar signals in noise, covering point targets, random process and scatter channels
Detection, estimation and linear modulation theory, Part 1, covering random processes, signal detection in noise and continuous waveforms
Equalization of dispersive channels using decision feedback, and state variable estimation of sonar or seismic data in presence of pure delay
Message estimation of sample function from continuous Gaussian random process, establishing and evaluating optimal bounds for procedure
Analog communication over randomly time varying channels
Optimum realizable linear filter role in some communication problems, considering detection and continuous estimation
Differential equation technique of representing dynamic systems for optimal control problems, and fundamental role of optimum linear filter
Transmission of analog message over channel corrupted by additive Gaussian noise, using modulation of sinusoidal carrier
Analog message transmission by optimum angle modulation system and rate distortion function deriving mean square error
Generalization of superposition principle of statistical communication theory & investigation of class of nonlinear systems
Analog communication over randomly time varying channels
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A model of a phase-locked loop has been developed which is valid for all signal-to-noise ratios. The model is in the form of a nonlinear feedback system with randomly time-varying parameters. The analysis considers two operating regions. In low signal-to-noise ratio regions, the important consideration is stability. We want to study the asymptotic stability in the mean of a nonlinear system. It follows directly that a necessary condition for asymptotic stability of any nonlinear system is that a linearized model about some equilibrium point be asymptotically stable. By considering all possible equilibrium points, we can find an upper bound on the value of noise density which makes the system unstable. This upper bound represents a threshold value for system operation. In high signal-to-noise ratio regions, our results provide an exact statistical. description of system behavior. Therefore, knowledge of the spectrum of the signal and noise may be used to optimize the system configuration.