Group representation theory and radar ambiguity functions

Kama, Eren Berk
In this thesis, representations of Heisenberg group are applied to ambiguity functions and their properties are investigated in with an information theoretic perspective with applications in telecommunications and signal processing. Algebraic properties of ambiguity functions were investigated through application of representation theory. Novel approaches on phase space tiling are given and some existing methods for traditional ambiguity functions were extended to MIMO ambiguity functions. Irreducible representations are used to obtain an orthonormal basis of L2(R2). An identity on different functions having same ambiguity function is used in MIMO case. Uncertainty relations on ambiguity functions and certain time frequency distributions are studied. Relations between norms of MIMO ambiguity functions and norms of signals creating them are given. A local uncertainty relation on MIMO ambiguity functions and a bound on delay Doppler support is given. Lieb uncertainty is used in MIMO ambiguity functions to obtain a sharp uncertainty relation. These uncertainty relations are connected with applications in time frequency analysis, compressed sensing and integrated sensing and communication applications. Moreover, uncertainty relations on Wigner distributions and marginalizable time frequency distributions are given. Uncertainty relation of de Bruijn was used on time frequency distributions with signal processing examples. Effect of symplectic transformations on Wigner Distributions was investigated. Actions of generators of SL(2,R) are tied with common signal processing operations and their effect on uncertainty was investigated. This effect and its applications in time frequency analysis and localization tasks are discussed. Furthermore, applications of time frequency analysis in quantum information theory and quantum harmonic analysis are discussed.


Fixed-frequency slice computation of discrete Cohen's bilinear class of time-frequency representations
Ozgen, MT (2000-02-01)
This communication derives DFT-sample-based discrete formulas directly in the spectral-correlation domain for computing fixed-frequency slices of discrete Cohen's class members with reduced computational cost, both for one-dimensional and multidimensional (specifically two-dimensional (2-D)) finite-extent sequence cases. Frequency domain integral expressions that define discrete representations are discretized to obtain these discrete implementation formulas. 2-D ambiguity function domain kernels are chosen...
A representation theorem for quantum systems
Dosi, Anar (Springer Science and Business Media LLC, 2013-07-01)
In this note representations of quantum systems are investigated. We propose a unital bipolar theorem for unital quantum cones, which plays a key role in proving a representation theorem for quantum systems. It turns out that each quantum system is identified with a certain quantum L-a-system up to a quantum order isomorphism.
Optical absorption of a quantum well with an adjustable asymmetry
Yildirim, H.; Tomak, Mehmet (Springer Science and Business Media LLC, 2006-04-01)
The effects of asymmetry and the electric field on the electronic subbands and the nonlinear intersubband optical absorption of GaAs quantum wells represented by a Poschl-Teller confining potential are studied. The potential itself can be made asymmetric through a correct choice of its parameter set and this adjustable asymmetry is important for optimizing the absorption. In that way optimal cases can be created. We calculate the modified wave functions and electronic subbands variationally. The linear and ...
Linear Separability Analysis for Stacked Generalization Architecture
Ozay, Mete; Vural, Fatos T. Yarman (2009-04-11)
Stacked Generalization algorithm aims to increase the individual classification performances of the classifiers by combining the information obtained from various classifiers in a multilayer architecture by either linear or nonlinear techniques. Performance of the algorithm varies depending on the application domains and the space analyses that affect the classification performances could riot be applied successfully.
Conformal perfectly matched absorbers in finite element mesh truncation
Kuzuoğlu, Mustafa; Mittra, R (2000-07-21)
In the numerical solution of electromagnetic scattering and/or radiation problems by finite methods, a mesh truncation scheme must be employed in order to obtain a bounded computational domain. We discuss the realization of perfectly matched absorbers by means of a complex coordinate transformation in a general coordinate system. In this way, it is possible to design perfectly matched layers (PMLs) which are conformal to the antenna/scatterer surface. The performance of the PMLs are tested for certain probl...
Citation Formats
E. B. Kama, “Group representation theory and radar ambiguity functions,” M.S. - Master of Science, Middle East Technical University, 2022.