Signal Processing Selected Topics

About the Book: Signal Processing Selected Topics This book discusses some of the important modern problems in signal processing. These topics are (1) Group theory and image processing in which the theory of group representations is applied to estimate how an image gets transformed when a noisy version of the transformed image is measured. (2) Quantum signal processing in which design of quantum gates by perturbing physical systems like atoms and oscillators with random forces like electromagnetic fields is discussed. The Heisenberg and Schrodinger equations for quantum systems in noise are also discussed with application to estimating the parameters of the Hamiltonian. Box quantization of fields is also discussed in this chapter. (3) Large deviation theory, in which asymptotic probabilities of rare events are computed using Cramers idea of rate functions. The rate functions of various random variables and processes are computed in this chapter. These rate functions enable us to compute probabilities of events like escape of a dynamical system perturbed by low amplitude noise from a boundary. The Gartner-Ellis theorem and Varadhans integral lemma are discussed the latter being a useful tool for computing the partition function in statistical mechanics at low temperatures. (4) Nonlinear and random problems in circuit theory are discussed using a perturbation theoretic approach. These are applied to transistor and diode circuits. The stochastic differential equation approach has been emphasized here. We have also considered frequency domain analysis of nonlinear systems. Some problems in hydrodynamics have been discussed like how a galactic patch moving according to the Navier-Stokes equation emits Doppler shifted radiation. Finally, problems in Einsteins general theory of relativity when the metric is randomly perturbed have been discussed. These include statistical properties of geodesics in a random metric, statistical properties of electromagnetic radiation in in