Covariance Sequence Approximation with Applications to Spectrum Analysis and Digital Filter Design.
Abstract
Modeling and estimation procedures for covariance sequence and spectrum approximation are developed in this thesis. The covariance sequence is modeled as a complex linear combination of damped complex exponentials. This model arises naturally as the representation for the covariance sequence associated with a strictly proper ARMA(M,N) system driven by white noise. Related to this seemingly natural covariance model is a synthesis procedure for a subclass of wide sense stationary ARMA(M,N) processes. The resulting spectral representation for the covariance sequence is a positive real linear combination of damped complex exponentials, a generalization of the standard representation in terms of stochastic almost periodic functions. The importance of the generalized structure lies in the more efficient representation of a large class of wide sense stationary processes. For this parametric approach estimation techniques are developed that lie in philiosophy somewhere between the nonlinear least squares approach and the tractable modified least squares procedure. The resulting parameter estimation equations are linear, except for a single polynominal rootfinding problem that must be solved.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA072884
Entities
People
- A. A. Beex
- Louis L. Scharf
Organizations
- Colorado State University