Smoothing

In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing.

Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways:

Monophthongization

Monophthongization is a sound change by which a diphthong becomes a monophthong, a type of vowel shift. In languages that have undergone monophthongization, digraphs that formerly represented diphthongs now represent monophthongs. The opposite of monophthongization is vowel breaking.

English

Some English sounds that may be perceived by native speakers as single vowels are in fact diphthongs; the vowel sound in pay — pronounced /ˈpeɪ/ — is an example of this. However, in some dialects (e.g. Scottish English) /eɪ/ is a monophthong [e].

Some dialects of English make monophthongs out of former diphthongs. For instance, Southern American English tends to realize the diphthong /aɪ/ as in eye as a long monophthong [äː].

Smoothing

In Received Pronunciation, when a diphthong is followed by schwa (or possibly by an unstressed /ɪ/), a series of simplifying changes may take place, sometimes referred to as smoothing.

To begin with, the diphthong may change to a monophthong, by dropping of the second element and slight lengthening of the first element: /aɪ/→[aː], /aʊ/→[ɑː], /eɪ/→[eː], /əʊ/→[ɜː]. The vowels /iː/ and /uː/, whose usual forms are in fact slightly diphthongal (close to [ɪi], [ʊu]), may undergo the same change and become [ɪː], [ʊː].

Smoothing (disambiguation)

Smoothing is the reduction or elimination in the roughness or unevenness of a surface or other thing.

Smoothing may refer to:

See also