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  1. IRE Transactions on Information Theory
  2. Year : 1956 Volume : 2
  3. Issue 1
  4. Interpolation and extrapolation of sampled data
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Year : 1962 Volume : 8
Year : 1961 Volume : 7
Year : 1960 Volume : 6
Year : 1959 Volume : 5
Year : 1958 Volume : 4
Year : 1957 Volume : 3
Year : 1956 Volume : 2
Issue 4
Issue 3
Issue 2
Issue 1
The bandwagon (Edtl.)
The probability distribution for the filtered output of a multiplier whose inputs are correlated, stationary, Gaussian time-series
Interpolation and extrapolation of sampled data
Report on the third London Symposium on Information Theory
Some optimal signals for time measurement
An analysis of signal detection and location by digital methods
Inverse probability in angular-tracking radars
The linear, input-controlled, variable-pass network
Rebuttal to comments by A. Jeffrey
Year : 1955 Volume : 1

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Interpolation and extrapolation of sampled data

Content Provider IEEE Xplore Digital Library
Author Lees, A.
Copyright Year 1955
Description This paper is essentially an extension of the optimum filtering theory of Zadeh and Ragazzini to the case where the time function to be operated upon is available only at a sequence of sample instants. As in the latter paper the signal is taken to consist of two parts, one being a polynomialp(t)with unknown coefficients and known maximum degreen, and the other being a stationary random componentM(t)with known autocorrelation function. It is assumed that the signal has been contaminated before filtering by the addition of stationary random noise, also of known autocorrelation function, and that the input to the filter consists of a sequence of impulse functions of constant repetition periodT, each impulse being of area equal to the sample value of the signal plus noise at the time of occurrence of the impulse. This paper shows how to find the weighting function,W(t), of a linear filter which will convert the sequence of impulse functions into a smoothed output subject to the following conditions: the weighting functionW(t)is only nonzero over a finite range; in the absence of random components, the interpolation or extrapolation is error-free; in the presence of any random signal the approximation at the output follows a least squares law. The weighting function of the optimum filter is shown to be piece-wise continuous in the intervals\{\gamma T \leq t \leq (\gamma + 1)T; \gamma = 0, 1, 2, \cdots N\}and the paper concludes with a discussion of a simple example illustrating the practical application of the solution.
Starting Page 12
Ending Page 17
Page Count 6
File Size 817569
File Format PDF
ISSN 00961000
Volume Number 2
Issue Number 1
Language English
Publisher Date 1956-03-01
Access Restriction Subscribed
Rights Holder Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword Interpolation Extrapolation Nonlinear filters Filtering theory Polynomials Least squares approximation Signal processing Autocorrelation Sampling methods Switches
Content Type Text
Resource Type Article
Subject Library and Information Sciences Information Systems Computer Science Applications
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