On linear weak predictability with single point spectrum degeneracy

Abstract

Listen

Translate article

The paper studies predicting problems for continuous time signals with the Fourier transforms vanishing with a certain rate at a single point. It shows that, with some linear causal predictors, anticausal convolution integrals over future times for these processes can be approximated by causal convolutions over past times. The corresponding predicting kernels are time invariant, and they are presented explicitly in the frequency domain via their transfer functions. These predictors are “universal” meaning that they do not require to know details of the spectrum of the underlying signals; the same predictor can be used for the entire class of signals with a single point spectrum degeneracy. The predictors feature some robustness with respect to noise contamination.