# Accession Number:

## ADA128278

# Title:

## Overspecified Normal Equations for Spectral Estimation.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## RESIN RESEARCH LABS INC NEWARK N J

# Personal Author(s):

# Report Date:

## 1983-06-01

# Pagination or Media Count:

## 74.0

# Abstract:

There is one-to-one relationship between a set of P normalized positive definite correlation estimates and the P predictor coefficients derived using autoregressive modeling. Several researchers have proposed the use of M greater than P corrrelation estimates to provide a better Pth order model. Specifically, the normal equations are augmented to provide M linear equations between the correlation estimates and the predictor coefficients. Since the system of equations is now overspecified, a least squares solution is required. In this thesis a study is presented of some of the properties of the method of overspecified normal equations as applied to the problem of spectral estimation. The main contribution of this thesis is the derivation of the relationships between the number of correlations used, the model order and the signal to noise ratio of the signal, to the characteristics of the resulting spectral estimate. The characteristics studied are the spectral height, bandwidth and area. The method is shown to be a spectral density estimator like the ME method, where spectral areas rather than spectral values should be interpreted as estimates of power.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Radiofrequency Wave Propagation