Reconstruction of nonuniformly sampled time-limited signals using prolate spheroidal wave functions

Şenay, Seda; Chaparro, Luıs F.; Durak, Lütfiye

doi:10.1016/j.sigpro.2009.04.020

Cited by 47 publications

(28 citation statements)

References 19 publications

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“…In other words, the Shannon sampling theorem states that in order to ensure accurate representation and reconstruction of a signal with Ω max , we should sample it at least at 2Ω max samples per second (i.e., the Nyquist rate). However, many recent publications have challenged this approach for a number of reasons (e.g., [44,45]). First, by using the Shannon sampling theorem we rely on bases of infinite support, while we generally reconstruct signal samples in the finite domain [44].…”

Section: Proposed Schemementioning

confidence: 99%

“…However, many recent publications have challenged this approach for a number of reasons (e.g., [44,45]). First, by using the Shannon sampling theorem we rely on bases of infinite support, while we generally reconstruct signal samples in the finite domain [44]. Second, large bandwidth values can severely constraint sampling architectures [45].…”

Section: Proposed Schemementioning

confidence: 99%

“…The problem is them to find the parameterst m that satisfy the above equation from the noisy nonuniform samples, which can be achieved using the annihilating filter [2,44,54]. In particular, if the transfer function of the annihilating filter is defined as…”

Section: Estimation Of Sampling Timesmentioning

confidence: 99%

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Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences

Sejdić

Can

Chaparro

et al. 2012

EURASIP J. Adv. Signal Process.

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Monitoring physiological functions such as swallowing often generates large volumes of samples to be stored and processed, which can introduce computational constraints especially if remote monitoring is desired. In this article, we propose a compressive sensing (CS) algorithm to alleviate some of these issues while acquiring dual-axis swallowing accelerometry signals. The proposed CS approach uses a time-frequency dictionary where the members are modulated discrete prolate spheroidal sequences (MDPSS). These waveforms are obtained by modulation and variation of discrete prolate spheroidal sequences (DPSS) in order to reflect the time-varying nature of swallowing acclerometry signals. While the modulated bases permit one to represent the signal behavior accurately, the matching pursuit algorithm is adopted to iteratively decompose the signals into an expansion of the dictionary bases. To test the accuracy of the proposed scheme, we carried out several numerical experiments with synthetic test signals and dual-axis swallowing accelerometry signals. In both cases, the proposed CS approach based on the MDPSS yields more accurate representations than the CS approach based on DPSS. Specifically, we show that dual-axis swallowing accelerometry signals can be accurately reconstructed even when the sampling rate is reduced to half of the Nyquist rate. The results clearly indicate that the MDPSS are suitable bases for swallowing accelerometry signals.

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Section: Proposed Schemementioning

confidence: 99%

Section: Proposed Schemementioning

confidence: 99%

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Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences

Sejdić

Can

Chaparro

et al. 2012

EURASIP J. Adv. Signal Process.

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“…In [3], the authors show how to reconstruct the original signal from the output of the ASDM. In the present work we provide a computationally efficient reconstruction algorithm based on a Prolate Spheroidal Wave Functions (PSWF) projection of the original signal [7], [9]. We show that many signals such as the electroencephalogram (EEG), can be accurately represented by the PSWFs as an interpretation of Shannon's sampling theory using the ASDM time codes.…”

Section: Introductionmentioning

confidence: 99%

Time encoding and reconstruction of multichannel data by brain implants using asynchronous sigma delta modulators

Şenay

Chaparro

Sclabassi

et al. 2009

2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Recently, information technology and microelectronics have enabled implanting miniature and highly intelligent devices within the brain for in-vitro diagnostic and therapeutic functions. Power and physical size constraints of these devices necessitate novel signal processing methods. In this paper we investigate an effective data acquisition and reconstruction method for brain implants based on Asynchronous Sigma Delta Modulators (ASDMs). The ASDMs are analog non-linear feedback systems capable of time coding signals. The proposed reconstruction algorithm is based on the Prolate Spheroidal Wave Function (PSWF) expansion of the sinc functions and the order of expansion is given by the input signal being coded. Multiplexing and transmission of the different channels of data are accomplished by chirp orthogonal frequency division multiplexing. Computer simulations using multi channel electroencephalographic data are performed for wireless transmission by brain implants for monitoring abnormal brain activities of epilepsy patients.

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“…[30,53,54] and also [47] with references therein. However, no proof of the restricted isometry property or the exact recovery of sparse signals appears.…”

Section: Introductionmentioning

confidence: 99%

Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions

Gosse¹

2012

Ann Univ Ferrara

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Reconstruction of nonuniformly sampled time-limited signals using prolate spheroidal wave functions

Cited by 47 publications

References 19 publications

Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences

Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences

Time encoding and reconstruction of multichannel data by brain implants using asynchronous sigma delta modulators

Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions

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