Problem conditioning interpolation educational tool
13 Mar 2013-pp 996-1003
TL;DR: This paper presents an educational tool to be used in signal processing interpolation-related subjects that allows its users to apply three error patterns geometry to the signals and test minimum dimension and maximum dimension signal reconstruction algorithms.
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.
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01 Jan 1983
34,729 citations
"Problem conditioning interpolation ..." refers methods in this paper
...To better understand and control the problem conditioning, in the presented tool, some new parameters are calculated: the spectral radius of the S matrix, delimited in (7) and the Condition Number of the (I-S) matrix (8) [2] [3]....
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...Still a great advantage of this tool is the possibility of a previous set up of the problem condition through the analysis of the spectral radius of the iteration matrix (in the case of iterative methods are used) and the computation of condition number in the case of the direct method solvers [2] [3]....
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Book•
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21,163 citations
"Problem conditioning interpolation ..." refers background in this paper
...In order to be effective, important educational and psychological issues were taken into account on designing it [7] [8]....
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TL;DR: In this paper, a new algorithm is proposed for computing the transform of a band-limited function, which is a simple iteration involving only the fast Fourier transform (FFT), and it is shown that the effect of noise and the error due to aliasing can be controlled by early termination of the iteration.
Abstract: If only a segment of a function f (t) is given, then its Fourier spectrum F(\omega) is estimated either as the transform of the product of f(t) with a time-limited window w(t) , or by certain techniques based on various a priori assumptions. In the following, a new algorithm is proposed for computing the transform of a band-limited function. The algorithm is a simple iteration involving only the fast Fourier transform (FFT). The effect of noise and the error due to aliasing are determined and it is shown that they can be controlled by early termination of the iteration. The proposed method can also be used to extrapolate bandlimited functions.
1,034 citations
Book•
14 Jan 1991TL;DR: This work treats numerical analysis from a mathematical point of view, demonstrating that the many computational algorithms and intriguing questions of computer science arise from theorems and proofs.
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982 citations
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TL;DR: In this article, preliminary concepts of frequency distribution, Percentiles, and Percentile Ranks Central Tendency Variability The Normal Curve Derived Scores Correlation Prediction Interpretive Aspects of Correlation and Regression Probability The Basis of Statistical Inference Further Considerations in Hypothesis Testing Testing Hypotheses about the Difference Between Two Independent Means Testing hypotheses about the difference between Two Dependent Means Power and Measure of Effect Size One-Way Analysis of Variance (and Some Alternatives).
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409 citations
"Problem conditioning interpolation ..." refers background in this paper
...In order to be effective, important educational and psychological issues were taken into account on designing it [7] [8]....
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