Problem conditioning interpolation educational tool

Abstract

This paper presents an educational tool to be used in signal processing interpolation-related subjects. Besides the consolidation of acquired theoretical knowledge, the tool allows its users to apply three error patterns geometry to the signals and test minimum dimension and maximum dimension signal reconstruction algorithms. In the specific case of minimum dimension problems it can be solved using different solvers, iterative and direct linear equations methods. The developed tool allows the problem conditioning analysis through the spectral radius of the system matrix, the condition number and others parameters available in some specific methods. This feature gives the possibility to alter the problem definitions to the desired goal before the reconstruction begins and to choose the optimal method, depending on each problem constraints The time unit that measures the algorithms performance is expressed in terms of one Fourier Transform (FFT) calculation time. In this way the data is presented not in an absolute way but in a relative measure independent from the machine's architecture.