The Asymptotic Behaviour of the $m$-th Order Cardinal $B$-Spline wavelet

TL;DR

This paper precisely characterizes the exponential decay rate of the $m$-th order cardinal $B$-spline wavelet, providing detailed insights into its asymptotic behavior.

Contribution

It determines the exact decay rate of the $m$-th order cardinal $B$-spline wavelet, advancing understanding of its asymptotic properties.

Findings

Exact decay rate of the wavelet is established.

Asymptotic behavior of the wavelet is fully described.

Provides theoretical foundation for wavelet decay analysis.

Abstract

It is well-known that the $m$-th order cardinal $B$-spline wavelet, $\psi_{m},$ decays exponentially. Our aim in this paper is to determine the exact rate of this decay and thereby to describe the asymptotic behaviour of $\psi_{m}$.