2016/09/04 by Cuiming Zou, Kit Ian Kou, Zou, Cuiming +3
Computer Science · Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geophysics and Sensor Technology #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1609.00891
openalex publication_date 2016/09/04 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28
One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should, therefore, be of great interest to find the most energy concentration hypercomplex signal. The present paper finds a new kind of hypercomplex signals whose energy concentration is maximal in both time and frequency under quaternionic Fourier transform. The new signals are a generalization of the prolate spheroidal wave functions (also known as Slepian functions) to quaternionic space, which are called quaternionic prolate spheroidal wave functions. The purpose of this paper is to present the definition and properties of the quaternionic prolate spheroidal wave functions and to show that they can reach the extreme case in energy concentration problem both from the theoretical and experimental description. In particular, these functions are shown as an effective method for bandlimited signals extrapolation problem.