Title :
Stationarity of the Gabor basis and derivation of Janssen´s formula
Author :
Polyak, Nikolay ; Pearlman, William A.
Author_Institution :
Dept. of Electr.-Comput.-Syst. Eng., Rensselaer Polytech. Inst., Troy, NY, USA
Abstract :
The theory of stationary processes is applied to homogeneous functional sequences. Examples of time and frequency shifts and dilations are considered. It is proved that the functional sequences are homogeneous (stationary) and therefore correspond to a one-dimensional stationary vector field. The spectral properties of these sequences are explored. It is also shown that the Gabor expansion corresponds to a two-dimensional homogeneous vector field. The spectral properties of the Gabor (1946) expansion are considered, and the formula for the coefficients of the Gabor decomposition is derived
Keywords :
spectral analysis; vectors; Gabor basis; Gabor decomposition coefficients; Gabor expansion; Janssen formula; dilations; frequency shifts; homogeneous functional sequences; one-dimensional stationary vector field; spectral properties; stationary processes; stationary sequences; time shifts; two-dimensional homogeneous vector field; Autocorrelation; Discrete transforms; Fourier transforms; Frequency; Kernel; Linear approximation; Stochastic processes; Systems engineering and theory; Technological innovation; Vectors;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1992., Proceedings of the IEEE-SP International Symposium
Conference_Location :
Victoria, BC
Print_ISBN :
0-7803-0805-0
DOI :
10.1109/TFTSA.1992.274135
