Nyquist-Shannon sampling theorem
farbin-e nemunân-giri-ye Nyquist-Shannon
Fr.: théorème d'échantillonnage de Nyquist-Shannon
The minimum number of resolution elements required to properly sample a signal, such as a star image, without causing erroneous effects known as aliasing. For electronic imaging, this number is generally taken as 2 pixels across the seeing disk diameter at the half intensity points. Also called → Shannon's sampling theorem and → sampling theorem.
Named after Harry Nyquist (1889-1976), a Swedish-born American physicist, who made important contributions to information theory, and Claude Elwood Shannon (1916-2001), an American mathematician and pioneer of information theory; → theorem.
The process of sampling a signal with a frequency higher than the → Nyquist frequency. The signal is said to be oversampled β times, where the oversampling ratio is defined as β = (sampling frequency)/(Nyquist frequency).
The act, process, or technique of selecting a number of cases from all the cases in a particular population.
Nemunân-giri, literally "taking sample," from nemunân→ sample + giri verbal noun of gereftan "to take, seize, hold;" Mid.Pers. griftan, gir- "to take, hold, restrain;" O.Pers./Av. grab- "to take, seize," cf. Skt. grah-, grabh- "to seize, take," graha- "seizing, holding, perceiving," M.L.G. grabben "to grab," from P.Gmc. *grab, E. grab "to take or grasp suddenly;" PIE *ghrebh- "to seize."
Fr.: biais de l'échantillonnage
That part of the difference between the expected value of the sample estimator and the true value of the characteristic which results from the sampling procedure, the estimating procedure, or their combination.
Fr.: erreur d'échantillonnage
That part of the difference between a population value and an estimate thereof, derived from a random sample, which is due to the fact that only a sample of values is observed; as distinct from errors due to imperfect selection, bias in response or estimation, errors of observation and recording, etc.
Fr.: théorème d'échantillonnage
Same as → Nyquist-Shannon sampling theorem.
Fr.: unité d'échantillonnage
One of the units into which an aggregate is divided for the purpose of sampling, each unit being regarded as individual and indivisible when the selection is made.
Shannon's sampling theorem
farbin-e nemunân-giri-ye Shannon
Fr.: théorème d'échantillonnage de Shannon
Same as → sampling theorem.
→ Shannon entropy; → sampling; → theorem.
The circumstance in which there are not enough pixels in a star's image. The number of pixels that make up a star's image is determined by the relationship between the telescope focal length, the physical size of the pixels, and the size of the star's image. With an undersampled image it is not possible to obtain accurate estimates of the star's image size or its position. Undersampling occurs when the atmospheric seeing conditions are exceptionally good and the pixel size not small enough.