Title :
An optimum complete orthonormal basis for signal analysis and design
Author :
Jin, Q. ; Luo, Z.Q. ; Wong, K.M.
Author_Institution :
Commun. Res. Lab., McMaster Univ., Hamilton, Ont., Canada
fDate :
5/1/1994 12:00:00 AM
Abstract :
Derives a new set of basis functions which have high energy concentration in both time and frequency. The approach is based on transforming a signal energy maximization problem into an equivalent eigenvalue problem for a certain integral operator, and then showing that the eigenvectors of this integral operator form a complete orthonormal basis. This basis set is in some sense optimal since each basis function has the highest energy concentration within a certain subspace of L2. Furthermore, this basis can be employed to analyze and design communication signals for which the energy concentration within the essential duration and essential bandwidth is important and some other optimum characteristics would also be required
Keywords :
eigenvalues and eigenfunctions; optimisation; signal processing; bandwidth; basis functions; communication signals; duration; eigenvectors; energy concentration; equivalent eigenvalue problem; integral operator; optimum complete orthonormal basis; signal analysis; signal design; signal energy maximization problem; Bandwidth; Channel capacity; Dispersion; Distortion; Eigenvalues and eigenfunctions; Fourier transforms; Frequency; Information rates; Signal analysis; Signal design;
Journal_Title :
Information Theory, IEEE Transactions on