This thesis consists of four chapters. The first two chapters pertain to the design of stable quantization methods for analog to digital conversion, while the third and fourth chapters concern problems related to compressive sensing. In the first chapter, we study the β-encoder and golden ratio encoder, and show that these quantization schemes are robust with respect to uncertainty in the multi...

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

--Timebase distortions cause nonlinear distortions of the sampled waveforms by equivalent-time sampling instruments. A new model of quantizer is proposed to be used when a large part of timebase distortions is the result of non-random quantization error that is known. A compensation method based on this model is applied to timebase quantization. The simulated results show that the proposed comp...

We consider the case of electromagnetic field inside a rectangular cavity with conducting walls as form system described by classical mechanics equations. pass these equations through Lagrangian formalism to obtain Hamiltonian formulation. Finally we apply canonical quantization end up quantum theory field. Since electrodynamics can be interpreted one photon system, then above is taken “quant...