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.

Problem conditioning interpolation educational tool

This work presents a newer and more complete version of an educational tool to be used in signal processing interpolation-related subjects. Besides the consolidation of acquired theoretical knowledge, the tool allows now its users to apply three error geometry patterns, test minimum or maximum dimension signal reconstruction algorithms and problem conditioning through the analysis of the matrix spectral radius or the condition number: these new features gives the possibility to alter the problem definitions to the desired goal before the reconstruction begins. The time unit that measures the algorithms performance is ¶(nlogn) thus independent from the machine’s architecture. A video of the developed tool can be seen in: https://www.dropbox.com/s/t6yiiuy31ramxse/FILME_1.avi.

https://www.ccsenet.org/journal/index.php/mas/article/download/32112/18689

Signal Processing Interpolation and Problem Conditioning Educational Workbench

In this correspondence, we derive the relationship between the eigenvalues associated with the matrices of the minimum dimension time-domain and frequency-domain approaches used for reconstructing missing uniform samples. The dependency of the eigenvalues of the weighted Toeplitz matrix on positive weights are explored. Simple bounds for the maximum and minimum eigenvalues of the weighted Toeplitz matrix are also presented. Alternative matrices possessing the same nonzero eigenvalues as that of the weighted Toeplitz matrix are provided. We verify the theory by the examples presented.

On the Eigenvalues of Matrices for the Reconstruction of Missing Uniform Samples

In this paper, we present a robust and efficient structure for the reconstruction of uniform samples of a signal from its recurrent nonuniform samples. This structure makes use of the synthesis part of a uniform discrete Fourier transform (DFT) modulated filterbank. The proposed structure is a refinement over an existing filterbank structure that utilizes the inverse of a nonuniform DFT matrix, the numerical stability of which cannot be guaranteed. The poor numerical stability of the inverse is overcome in a modified structure by inverting a preconditioned matrix having an improved numerically stable inverse. Necessary and sufficient conditions that ensure numerical stability of the preconditioned matrix inverse have been presented.

M. Karthik

Papers

On the Eigenvalues of Matrices for the Reconstruction of Missing Uniform Samples

Robust and efficient filterbank structure for reconstruction from recurrent nonuniform samples