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The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.
Pass and stop bands of a filter designed by the Parks–McClellan algorithm The y-axis is the frequency response H(ω) and the x-axis are the various radian frequencies, ω i. It can be noted that the two frequences marked on the x-axis, ω p and ω s. ω p indicates the pass band cutoff frequency and ω s indicates the stop band cutoff ...
However, it is used in conceptual demonstrations or proofs, such as the sampling theorem and the Whittaker–Shannon interpolation formula. Sinc-in-time filters must be approximated for real-world (non-abstract) applications, typically by windowing and truncating an ideal sinc-in-time filter kernel, but doing so reduces its ideal properties. [2]
In statistics, DFFIT and DFFITS ("difference in fit(s)") are diagnostics meant to show how influential a point is in a linear regression, first proposed in 1980. [ 1 ] DFFIT is the change in the predicted value for a point, obtained when that point is left out of the regression:
Far from the cutoff frequency in the transition band, the rate of increase of attenuation with logarithm of frequency is asymptotic to a constant. For a [[Low-pass filter#:~:text=information: Electronic filter-,First-order passive,-[edit]|first-order]] network, the roll-off is −20 dB per decade (approximately −6 dB per octave .)
Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem.
In asymptotic analysis in general, one sequence () that converges to a limit is said to asymptotically converge to with a faster order of convergence than another sequence () that converges to in a shared metric space with distance metric | |, such as the real numbers or complex numbers with the ordinary absolute difference metrics, if
In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to the concept of an ancillary statistic . While an ancillary statistic contains no information about the model parameters, a complete statistic contains only information about the parameters, and ...