On BT-limited Signals

TL;DR

This paper introduces BT-limited signals, a new subspace of bandlimited signals with specific Fourier transform properties, and provides methods for signal extrapolation with error estimates outside a given interval.

Contribution

The paper defines BT-limited signals, characterizes their properties, and develops extrapolation techniques with analytic error bounds for this new class.

Findings

BT-limited signals form a well-defined subspace with unique properties.

Signal extrapolation outside the known interval is possible with quantifiable error.

New applications and properties of BT-limited signals are demonstrated.

Abstract

In this paper, we introduce and characterize a subspace of bandlimited signals. The subspace consists of all $\Omega$ bandlimited signals such that the non-zero parts of their Fourier transforms are pieces of some $T$ bandlimited signals. The signals in the subspace are called BT-limited signals and the subspace is named as BT-limited signal space. For BT-limited signals, a signal extrapolation with an analytic error estimate exists outside the interval [-T, T] of given signal values with errors. Some new properties about and applying BT-limited signals are also presented.