An Investigation of Three Methods for Spectral Representation of Randomly Distributed Data,
Abstract
Three methods are proposed for representing randomly distributed data by a truncated Fourier series. These methods involve the use of: (1) a set of linear equations based on a simple least-squares approach; (2) empirical orthogonal functions derived by the Gram-Schmidt process; and (3) a step-by-step approach where each coefficient is solved independently by subtracting the contribution from previously computed coefficients. The methods are tested against a known function (finite cosine series) for different distributions of data and different truncation and simulated observation errors. Results show that if the empirical orthogonal functions are linear combinations of cosines, the Methods 1 and 2 yield identical coefficients. This offers two convenient methods for achieving the same goal, depending on the number of data points and the truncation. Results also indicate that Method 3 is not very sensitive to the number of data points or to their distributions while Methods 1 and 2 are, failing when the number of data points approaches the critical value for resolving the waves. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 21, 1981
- Accession Number
- ADA111854
Entities
People
- Isidore M. Halberstam