Signal to Noise Enhancement for Data use in LVD
Abstract
The basic problem addressed under this research is the development of a scheme for deconvolving a set of correlated signals in a multichannel scenario so as to assure signal to noise enhancement. The author addressed this problem during the previous work period via the development of the Karhunen Loeve transformation. The original purpose of this phase was to continue this linear of approach and to some extent this was achieved. However it became necessary to alter the course temporally for reasons to be discussed below. We really cannot continue in any serious way until we can evaluate numerically the highly oscillatory integrals that are an integral part of the analysis. The reason is that asymptotic evaluations of these integrals is simply not powerful enough to yield accurate numerical results; for the same reason expansions in special functions are also not very effective. Thus we are forced to consider sophisticated numerical techniques to evaluate the integrals; this is really a step forward because computers are not so fast that one can almost gain the speed of an FFT (which is known to be a reasonably inaccurate way to evaluate oscillatory integrals). To this end I have decided to concentrate upon the development of accurate numerical evaluation of zero and first order Hankel transforms as the majority of the integrals need to secure understanding of the Karhunen Loeve approach to the averaging process require such integrals. In addition, I have worked out a numerical scheme for evaluation of finite range Fourier integrals as such integrals appear in my approach to the laser doppler in the new FM analysis which supersedes the old George-Lumley approach. Thus there are two sections entitled: (1) Filon trapezoidal schemes for Hankel transforms of orders zero and one; (2) Numerical evaluation of Fourier integrals: Filon quadrature versus the FFT.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 22, 1998
- Accession Number
- ADA335477
Entities
People
- Richard Barakat
Organizations
- Tufts University