Title :
Scale, frequency, time, and the scale transform
Author_Institution :
Rutgers Univ., Piscataway, NJ, USA
Abstract :
The author develops the relationship between time, frequency, and scale, and their respective operators and representations. A scale operator is proposed and its eigenfunctions are obtained. This leads to the scale transform. The convolution and correlation theorems for scale are developed. The concepts of filtering and linear shift-invariant systems are formulated for scale
Keywords :
Fourier transforms; correlation theory; eigenvalues and eigenfunctions; filtering and prediction theory; linear systems; time-frequency analysis; convolution theorem; correlation theorem; eigenfunctions; filtering; frequency; linear shift-invariant systems; scale operator; scale transform; time; Convolution; Educational institutions; Eigenvalues and eigenfunctions; Equations; Filtering; Fourier transforms; Frequency domain analysis; H infinity control; Nonlinear filters;
Conference_Titel :
Statistical Signal and Array Processing, 1992. Conference Proceedings., IEEE Sixth SP Workshop on
Conference_Location :
Victoria, BC
Print_ISBN :
0-7803-0508-6
DOI :
10.1109/SSAP.1992.246836
