Sykulski, AM;
Percival, DB;
(2016)
Exact simulation of noncircular or improper complex-valued stationary Gaussian processes using circulant embedding.
In: Palmieri, F and Uncini, A and Diamantaras, K and Larsen, J, (eds.)
2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP).
Institute of Electrical and Electronics Engineers (IEEE)
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Abstract
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multi-variate Gaussian processes from the circulant embedding literature. The method can be performed in O(n log2 n) operations, where n is the length of the desired sequence. The method is exact, except when eigenvalues of prescribed circulant matrices are negative. We evaluate the performance of the algorithm empirically, and provide a practical example where the method is guaranteed to be exact for all n, with an improper fractional Gaussian noise process.
| Type: | Proceedings paper |
|---|---|
| Title: | Exact simulation of noncircular or improper complex-valued stationary Gaussian processes using circulant embedding |
| Event: | 2016 IEEE International Workshop On Machine Learning For Signal Processing, 13-16 September 2016, Salerno, Italy |
| ISBN-13: | 9781509007462 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/MLSP.2016.7738840 |
| Publisher version: | https://doi.org/10.1109/MLSP.2016.7738840 |
| Language: | English |
| Additional information: | Copyright © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
| Keywords: | Covariance matrices, Eigenvalues and eigenfunctions, Gaussian processes, Signal processing algorithms, Matrix decomposition, Gaussian noise, Fractional Gaussian noise, Circulant embedding, improper, noncircular, complex-valued |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1497773 |
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