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Non-Uniform Sampling in Statistical Signal Processing
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Non-uniform sampling comes natural in many applications, due to for example imperfect sensors, mismatched clocks or event-triggered phenomena. Examples can be found in automotive industry and data communication as well as medicine and astronomy. Yet, the literature on statistical signal processing to a large extent focuses on algorithms and analysis for uniformly, or regularly, sampled data. This work focuses on Fourier analysis, system identification and decimation of non-uniformly sampled data.

In non-uniform sampling (NUS), signal amplitude and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this thesis, the sampling times are assumed to be generated by a stochastic process, and the main idea is to use information about the stochastic sampling process to calculate a priori properties of approximate frequency transforms. These results are also used to give insight in frequency domain system identification and help with analysis of down-sampling algorithms.

The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Based on this, decimation of non-uniformly sampled signals, using continuous-time anti-alias filters, is analyzed. The decimation is based on interpolation in different domains, and interpolation in the convolution integral proves particularly useful. The same idea is also used to investigate how stochastic unmeasurable sampling jitter noise affects the result of system identification. The result is a modification of known approaches to mitigate the bias and variance increase caused by the sampling jitter noise.

The bottom line is that, when non-uniform sampling is present, the approximate frequency transform, identified transfer function and anti-alias filter are all biased to what is expected from classical theory on uniform sampling. This work gives tools to analyze and correct for this bias.

Place, publisher, year, edition, pages
Institutionen för systemteknik , 2007. , 76 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1082
Keyword [en]
signal processing, sampling, stochastic analysis, frequency transform
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-8480ISBN: 978-91-85715-49-7 (print)OAI: oai:DiVA.org:liu-8480DiVA: diva2:23251
Public defence
2007-05-11, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2009-04-26
List of papers
1. Frequency Domain Analysis of Signals with Stochastic Sampling Times
Open this publication in new window or tab >>Frequency Domain Analysis of Signals with Stochastic Sampling Times
2008 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 7, 3089-3099 p.Article in journal (Refereed) Published
Abstract [en]

In nonuniform sampling (NUS), signal amplitudes and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this paper, the sampling times are assumed to be generated by a stochastic process. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Specific sampling processes as described in literature are analyzed in detail. The results are illustrated on simulated signals, with particular focus to the implications for spectral estimation.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2008
Keyword
Fourier transforms, Frequency-domain analysis, Signal sampling, Stochastic processes, Alias suppression, Approximate Fourier transform, Frequency domain signal analysis, Nonuniform stochastic sampling time distribution
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-14326 (URN)10.1109/TSP.2008.917872 (DOI)
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2017-12-13
2. Identification with Stochastic Sampling Time Jitter
Open this publication in new window or tab >>Identification with Stochastic Sampling Time Jitter
2008 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 3, 637-646 p.Article in journal (Refereed) Published
Abstract [en]

This work investigates how stochastic sampling jitter noise affects the result of system identification, and proposes a modification of known approaches to mitigate the effects of sampling jitter, when the jitter is unknown and not directly measurable. By just assuming conventional additive measurement noise, the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies. A frequency domain approach with a continuous-time model allows an analysis framework for sampling jitter noise. The bias and covariance in the frequency domain model are derived. These are used in bias compensated (weighted) least squares algorithms, and by asymptotic arguments this leads to a maximum likelihood algorithm. Continuous-time output error models are used for numerical illustrations.

Place, publisher, year, edition, pages
Elsevier, 2008
Keyword
Non-uniform sampling, Sampling jitter, System identification, Stochastic systems, Maximum likelihood, Least squares estimation, Frequency domain, Parametric model
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-14327 (URN)10.1016/j.automatica.2007.06.018 (DOI)
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2017-12-13
3. Downsampling Non-Uniformly Sampled Data
Open this publication in new window or tab >>Downsampling Non-Uniformly Sampled Data
2008 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180Article in journal (Refereed) Published
Abstract [en]

Decimating a uniformly sampled signal a factor D involves low-pass antialias filtering with normalized cutoff frequency 1/D followed by picking out every Dth sample. Alternatively, decimation can be done in the frequency domain using the fast Fourier transform (FFT) algorithm, after zero-padding the signal and truncating the FFT. We outline three approaches to decimate non-uniformly sampled signals, which are all based on interpolation. The interpolation is done in different domains, and the inter-sample behavior does not need to be known. The first one interpolates the signal to a uniformly sampling, after which standard decimation can be applied. The second one interpolates a continuous-time convolution integral, that implements the antialias filter, after which every Dth sample can be picked out. The third frequency domain approach computes an approximate Fourier transform, after which truncation and IFFT give the desired result. Simulations indicate that the second approach is particularly useful. A thorough analysis is therefore performed for this case, using the assumption that the non-uniformly distributed sampling instants are generated by a stochastic process.

Place, publisher, year, edition, pages
Hindawi Publishing Corporation, 2008
Keyword
Decimation, Stochastic sampling, Signal processing
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-14328 (URN)10.1155/2008/147407 (DOI)
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2017-12-13

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