Alias-free sampling: An alternative conceptualization and its applications

Masry, E.

doi:10.1109/tit.1978.1055889

Cited by 90 publications

(80 citation statements)

References 7 publications

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“…These possibilities are exploited in the proposed HySt approach. It is noted that the convergence rate of an estimator satisfying Theorem 1 could be faster than The three stratified approaches StSa, AnSt and HySt considered here use stratification strategies defined by (16) and, as shown in this paper, they satisfy (21). Therefore, Lemma 1 is used to prove that assumption (A.4) of Theorem 1 holds for StSa, AnSt and HySt schemes.…”

Section: A Stratification In Ft Estimationmentioning

confidence: 98%

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Estimation of Fourier Transform Using Alias-Free Hybrid-Stratified Sampling

Tarczyński

Ahmad

2016

IEEE Trans. Signal Process.

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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.The WestminsterResearch online digital archive at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners.Whilst further distribution of specific materials from within this archive is forbidden, you may freely distribute the URL of WestminsterResearch: ((http://westminsterresearch.wmin.ac.uk/).In case of abuse or copyright appearing without permission e-mail repository@westminster.ac.uk  Abstract-This paper proposes a novel method of estimating the Fourier Transform (FT) of deterministic, continuous-time signals, from a finite number N of their samples taken from a fixed-length observation window. It uses alias-free hybridstratified sampling to probe the processed signal at a mixture of deterministic and random time instants. The FT estimator, specifically designed to work with this sampling scheme, is unbiased, consistent and fast converging. It is shown that if the processed signal has continuous third derivative, then the estimator's rate of uniform convergence in mean square is N^(-5). Therefore, in terms of frequency-independent upper bounds on the FT estimation error, the proposed approach significantly outperforms existing estimators that utilize alias-free sampling, such as total random, stratified sampling, and antithetical stratified whose rate of uniform convergence is N^(-1). It is proven here that N^(-1) is a guaranteed minimum rate for all stratifiedsampling-based estimators satisfying four weak conditions formulated in this paper. Owing to the alias-free nature of the sampling scheme, no constraints are imposed on the spectral support of the processed signal or the frequency ranges for which the Fourier Transform is estimated.

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Section: A Stratification In Ft Estimationmentioning

confidence: 98%

“…This notion was then revisited in various studies, e.g. [16], [17], and extended to the analysis of other classes of signals, and to target different signal processing objectives. The domain of signal processing that exploits alias-free sampling became known as Digital Alias-free Signal Processing (DASP).…”

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confidence: 99%

Estimation of Fourier Transform Using Alias-Free Hybrid-Stratified Sampling

Tarczyński

Ahmad

2016

IEEE Trans. Signal Process.

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“…Alias-free sampling is a type of non-uniform sampling technique where the set of sampling instants {tn} satisfies certain properties such that the spectrum of the resulting discrete WSS process avoids aliasing and/or yields consistent PSD estimates [8,9]. Typically, the set {tn} is a stochastic point process (e.g., a Poisson point process) that is statistically independent of the signal.…”

Section: Alias-free and Multi-coset Samplingmentioning

confidence: 99%

“…The proposed estimator also shares many aspects with digital alias-free signal processing (DASP) [8,9], and in particular, can be viewed as a type of DASP spectral estimator. The link with DASP is briefly examined in Sections 2 and 3.…”

Section: Introductionmentioning

confidence: 99%

Compressive power spectral density estimation

Lexa

Davies

Thompson

et al. 2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper, we consider power spectral density estimation of bandlimited, wide-sense stationary signals from sub-Nyquist sampled data. This problem has recently received attention from within the emerging field of cognitive radio for example, and solutions have been proposed that use ideas from compressed sensing and the theory of digital alias-free signal processing. Here we develop a compressed sensing based technique that employs multi-coset sampling and produces multi-resolution power spectral estimates at arbitrarily low average sampling rates. The technique applies to spectrally sparse and nonsparse signals alike, but we show that when the widesense stationary signal is spectrally sparse, compressed sensing is able to enhance the estimator. The estimator does not require signal reconstruction and can be directly obtained from a straightforward application of nonnegative least squares.

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“…Posterior analysis of AFTs in terms of alias suppression and leakage is a fairly well explored area (Lomb, 1976;Scargle, 1982;Wojtkiewicz and Tuszyński, 1992). The reverse problem of designing NUS to maximize alias suppression is also well studied (Papenfuss et al, 2003;Bland and Tarczynski, 1997;Shapiro and Silverman, 1960;Masry, 1978Masry, , 1983Hall and Yin, 2004).…”

Section: Introductionmentioning

confidence: 99%

Frequency Domain Analysis of Signals With Stochastic Sampling Times

Eng

Gunnarsson

Gustafsson

2008

IEEE Trans. Signal Process.

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In non-uniform 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. In non-uniform 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.

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Alias-free sampling: An alternative conceptualization and its applications

Cited by 90 publications

References 7 publications

Estimation of Fourier Transform Using Alias-Free Hybrid-Stratified Sampling

Estimation of Fourier Transform Using Alias-Free Hybrid-Stratified Sampling

Compressive power spectral density estimation

Frequency Domain Analysis of Signals With Stochastic Sampling Times

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