The Interpretation of Linear Prediction by Interpolation Framework and Several following Results

TL;DR

This paper offers a new interpolation-based interpretation of Linear Prediction, clarifies estimation mechanisms, introduces two novel LP construction methods, and explores the connection between LP and Taylor series.

Contribution

It presents a non-statistical interpretation of LP, proposes two new LP construction methods, and relates LP to Taylor series, enhancing understanding and application.

Findings

Least squares estimation of LP coefficients is intuitively explained.

LP coefficients cannot distinguish signals with the same interpolation bases.

Two new LP construction methods based on DCT-1 and difference operator are proposed.

Abstract

This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of widely used least square estimation of LP coefficients can be explained more intuitively. In data modeling, LP coefficients cannot distinguish signals spanned by the same interpolation bases. Two new general LP constructive methods instead of least square estimation are presented with their upper bounds of approximation error and some properties given; one is based on DCT-1 and the other is based on difference operator. We also establish the relationship between LP and Taylor series.