6533b858fe1ef96bd12b575b

RESEARCH PRODUCT

Mixed Convolutions and Zak Transforms

Amir AverbuchValery A. ZheludevPekka Neittaanmäki

subject

PolynomialPure mathematicsComputer Science::GraphicsIntegral representationCharacteristic function (probability theory)Fourier seriesExponential splineMathematics::Numerical AnalysisMathematics

description

In this chapter we introduce the mixed continuous–discrete and discrete–discrete convolutions. Important special cases of such convolutions are the polynomial and discrete splines, respectively. The Zak transforms, which are introduced in the chapter, provide integral representation of signals, which, in the following chapters, serves as a tool for the design of splines and spline-wavelets and operations over them. The exponential splines, which are the Zak transforms of polynomial and discrete B-splines are introduced. Explicit formulas for the characteristic functions of splines’ spaces are derived.

yearjournalcountryeditionlanguage
2015-08-28
https://doi.org/10.1007/978-3-319-22303-2_3