Polynomial Interpolation of Randomly Sampled Bandlimited Functions and Processes

Klamer, Dale M.; Masry, E.

doi:10.1137/0142071

Cited by 13 publications

(9 citation statements)

References 12 publications

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“…A natural question is whether it also offers an opportunity for estimating the signal accurately from only a block of samples. As interpolation of the signal between its samples has been discussed from several points of view [3], [5], we concentrate here on extrapolation beyond the interval of observation.…”

Section: Statement Of Resultsmentioning

confidence: 99%

Extrapolating a band-limited function from its samples taken in a finite interval

Landau¹

1986

IEEE Trans. Inform. Theory

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Section: Statement Of Resultsmentioning

confidence: 99%

Extrapolating a band-limited function from its samples taken in a finite interval

Landau¹

1986

IEEE Trans. Inform. Theory

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“…Klamer and Masry (1982), and Shapiro and Botha (1991) address the related problem of stationary isotropic variogram estimation for random fields. Hall et al (1994) use the Fourier characterization to obtain a positive definite kernel-type estimator.…”

Section: Related Literaturementioning

confidence: 99%

“…With random sampling schemes, Masry (1983) explores another kernel-type covariance estimator and Klamer and Masry (1982) consider the performance of the Lagrange polynomial interpolation.…”

Section: Related Literaturementioning

confidence: 99%

Non parametric estimation of smooth stationary covariance functions by interpolation methods

Elogne

Perrin²,

Thomas‐Agnan

2007

Stat Infer Stoch Process

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“…Specifically, we treat the deterministic scheduling to random access as periodic sampling with missing samples to random sampling. However, because the sampling dictated by the two MAC schemes comes from the specific sensor network application, the periodic and random sampling in our problem possess their own unique characteristics, and thus are different from the traditional sampling problem set up [2]- [8]. Therefore, the literature on the studies of sampling does not provide an answer to our problem.…”

mentioning

confidence: 49%

“…Let be the probability of sensor outage. For the target , the smallest interval length that enables should satisfy (6) In other words, the resolution interval is determined by and as (7) Notice that the maximum number of disjoint intervals that can enable is (8) In summary, for given target sensor outage probability and network density , the deterministic scheduler first sets the resolution interval length according to (7). For given slots of collection time ( ), it next enables intervals of length centered at the equally spaced locations.…”

Section: ) Deterministic Schedulermentioning

confidence: 99%

Information retrieval and processing in sensor networks: deterministic scheduling vs. random access

Dong

Tong

Sadler³

International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.

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Abstract-We investigate the effect of medium-access control (MAC) used in information retrieval by a mobile access point (AP) on information processing in large-scale sensor network, where sensors are unreliable and subject to outage. We focus on a 1-D sensor network and assume that the location information is available locally at each sensor and unavailable to the AP. For a fixed collection interval, two types of MAC schemes are considered: the deterministic scheduling, which collects data from predetermined sensors locations, and random access, which collects data from random locations. We compare the signal estimation performance of the two MACs, using the expected maximum distortion as the performance measure. For large sensor networks with fixed density, we show that there is a critical threshold on the sensor outage probability out : For out (1+ (1)) , where is the throughput of the random access protocol, the deterministic scheduling provides better reconstruction performance. However, for out (1+ (1)) , the performance degradation from missing data samples due to sensor outage does not justify the effort of scheduling; simple random access outperforms the optimal scheduling.

show abstract

Polynomial Interpolation of Randomly Sampled Bandlimited Functions and Processes

Cited by 13 publications

References 12 publications

Extrapolating a band-limited function from its samples taken in a finite interval

Extrapolating a band-limited function from its samples taken in a finite interval

Non parametric estimation of smooth stationary covariance functions by interpolation methods

Information retrieval and processing in sensor networks: deterministic scheduling vs. random access

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