Date of Award
Gabor Analysis, Time frequency, Wilson basis
Discrete orthonormal time-frequency basis functions are described and used for both analysis and synthesis of complex-valued signals. We derive expressions for complex-valued expansion coefficients in time-frequency lattices in the discrete one dimensional case. This derivation is based on Professor I. Gertner's previous construction of a complete orthonormal set of basis functions well localized in the temporal-spatial-frequency domain in the continuous case. We describe how these can be generalized to any number of dimensions. Example applications are presented in one and two dimensions. Three dimensional basis functions are visualized and discussed. Finally, a full a Matlab implementation of this work is provided. Chapter two of this thesis has been submitted for publication as a self-contained paper.
Chisholm, David, "DISCRETE TRANSFORMS WITH GOOD TIME-FREQUENCY AND SPATIAL-FREQUENCY LOCALIZATION" (2013). CUNY Academic Works.