Signal analysis. Representation tools (Q2711198)

In the thesis, two types of signal representations are considered, parameterized signal representations involving the entire signal domain (global signal properties) and local representations induced by short-term transformations (local properties). The bibliography contains 103 references. The main results are: NEWLINENEWLINENEWLINEIn part I, a nonlinear optimization problem is derived for selecting optimal parameters (in the sense that the representation of a signal with respect to an orthogonal system is condensed in an as small as possible number of elements of this system) for its global representation by using orthogonal series. Applications are given to Jacobi expansions, to harmonically modulated Laguerre/Hermite expansions and a recursive procedure for selecting optimal poles in Kautz expansions. NEWLINENEWLINENEWLINEPart II is concerned with local representation. A concept of sliding window unitary transformation is introduced and the concept of sliding window Fourier transformation is generalized. This type of transformation is analyzed in the setting of filter banks and frames and applied to Laguerre and Kautz systems. NEWLINENEWLINENEWLINETo suppress the artifacts at the transition boundaries, the discrete-time lapped orthogonal segmentation is studied in part III. In this connection a design methodology for (tight) frames is developed. A procedure for constructing a lapped orthogonal hexagonal segmentation is described.