Limited memory predictors based on polynomial approximation of periodic exponents

Abstract

The paper presents transfer functions for limited memory time-invariant linear integral predictors for continuous time processes such that the corresponding predicting kernels have bounded support. It is shown that processes with exponentially decaying Fourier transforms are predictable with these predictors in some weak sense, meaning that convolution integrals over the future times can be approximated by causal convolutions over past times. For a given predicting horizon, the predictors are based on polynomial approximation of a periodic exponent (complex sinusoid) in a weighted $L_2$-space.

References in corpus (2)

• Predictors for discrete time processes with energy decay on higher frequencies
• Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters

Cited by in corpus (2)

• Near-ideal predictors and causal filters for discrete time signals
• Predictors for high frequency processes based on rational polynomials approximation of periodic exponentials