Resampling and reconstruction with fractal interpolation functions

Abstract

An alternative form of the fractal interpolation function (FIF)-previously unmentioned in the signal processing literature-is noted. This form highlights a simple relationship between fractal and linear interpolation. Using this relationship, many FIF problems can be reduced to a matrix/vector expression. This expression provides a more powerful way to employ the FIF for interpolation and permits its adaptation for reconstruction. Additionally, the alternate form of the FIF allows the construction of fractal functions whose piecewise integrals match observed data.