6533b82efe1ef96bd1294534

RESEARCH PRODUCT

Non-periodic Discrete Splines

Amir AverbuchPekka NeittaanmäkiValery A. Zheludev

subject

UpsamplingComputer Science::GraphicsIntegral representationCharacteristic function (probability theory)ComputationZak transformApplied mathematicsSpecial caseInfinite impulse responseFourier seriesMathematics::Numerical AnalysisMathematics

description

Discrete Splines with different spans were introduced in Sect. 3.3.1. This chapter focuses on a special case of discrete splines whose spans are powers of 2. These splines are discussed in more detail. The Zak transform provides an integral representation of such splines. Discrete exponential splines are introduced. Generators of the discrete-spline spaces are described whose properties are similar to properties of polynomial-spline spaces generators. Interpolating discrete splines provide efficient tools for upsampling 1D and 2D signals. An algorithm for explicit computation of discrete splines is described.

yearjournalcountryeditionlanguage
2015-08-28
https://doi.org/10.1007/978-3-319-22303-2_9