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Novel Mathematical Expression for Spectrum Determination of Irregularly Sampled Data

by The Interpolation PublicationMarch 10th, 2024

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This conclusion unveils a novel mathematical expression for spectrum determination in irregularly sampled time-domain data, shedding light on interpolative methodologies and their applications in signal processing. Additionally, it highlights the availability of a software package for easy implementation in various signal processing applications.

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Authors:

(1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada;

(2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada;

(3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada;

(4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada.

Table of Links

Abstract & Introduction

Optimization of the Optical Interpolation

Materials and Methods

Results and Discussion

Conclusion

Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements

Appendix B: AAH ̸= MIN I in the Non-Equidistant Case

Acknowledgments & References

5 CONCLUSION

A convenient mathematical expression to solve for the spectrum of irregularly sampled time-domain data has been demonstrated in a way that satisfies the conditions for an inverse non-uniform Fourier transform. This methodology has been derived from cost function proposed in the original study, and via its idealised quadratic form strongly suggests that its minimum is unique and convex. Using a randomly sample time series from data with few missing values, the observed relative error is on the same order of magnitude as the most current solution to this problem [10]. Upon cross-validation with contiguous blocks, we report a relative error that is much higher, and suggest this is a more critical, but informative lens through which to view interpolation problems.

he proposed formula will find use in a variety of signal processing applications, where the use of an FFT is impractical given its assumption of a consistent time-domain density. The software package used in this work is available online: https://github.com/CoDaSLab/intrp infft 1d