A Comparison of Linear Bases for Pulsed Signals.
Abstract
Representation of a signal as a vector projected onto a finite linear orthogonal basis is a familiar geometrical technique for the analysis of pulsed signals. This study makes a comparison of a number of bases which have found use in the description of radar pulses. These bases may be separated into four classes; exponential functions, orthogonal polynomials, orthogonalized rectangular functions, and principal components. The exponential bases include the Fourier series, functions, based on Laguerre and Legendre polynomials, and Kautz functions with both real and complex exponents. Prony's method and the fast Fourier transform are used in selecting the Kautz exponents. The polynomial expansions include Chebyshev, Laguerre and Legendre polynomials. Bases formed from the Walsh and Haar orthogonal square waves have been included because of their relative simplicity of implementation. The method of principal components is used as a means for artificially generating a set of signals which collectively are uncorrelated with any given set. In making the comparison, both simulated and actual radar pulses are used. Plots of a number of signals reconstructed from these various expansions are illustrated in order to provide some insight into the suitability of these bases for pattern sorting purposes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1971
- Accession Number
- AD0880702
Entities
People
- R. S. Bennett
Organizations
- Johns Hopkins University