ISO 16610-29:2020 pdf download.Geometrical product specifications (GPS) — Filtration.
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16610-1, ISO 16610-20,
ISO 16610-22 and ISO/IEC Guide 99 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
mother wavelet
function of one or more variables which forms the basic building block for wavelet analysis, i.e. an
expansion of a signal/profile as a linear combination of wavelets
Note 1 to entry: A mother wavelet, which usually integrates to zero, is localized in space and has a finite bandwidth. Figure 1 provides an example of a real-valued mother wavelet.
3.1.1
biorthogonal wavelet
wavelet where the associated wavelet transform (3.3) is invertible but not necessarily orthogonal
Note 1 to entry: The merit of the biorthogonal wavelet is the possibility to construct symmetric wavelet functions,which allows a linear phase filter.
3.2.1 dilation <wavelet> transformation which scales the spatial variable x by a factor α Note 1 to entry: This transformation takes the function g(x) to α −0,5 g(x/α) for an arbitrary positive real number α. Note 2 to entry: The factor α −0,5 keeps the area under the function constant.
3.2.2 translation transformation which shifts the spatial position of a function by a real number b Note 1 to entry: This transformation takes the function g(x) to g(x − b) for an arbitrary real number b. 3.3 wavelet transform unique decomposition of a profile into a linear combination of a wavelet family (3.2)
3.4 discrete wavelet transform DWT unique decomposition of a profile into a linear combination of a wavelet family (3.2) where the translation (3.2.2) parameters are integers and the dilation (3.2.1) parameters are powers of a fixed positive integer greater than 1 Note 1 to entry: The dilation parameters are usually powers of 2.
3.5.2 high-pass component difference component component of the multiresolution analysis (3.5) obtained after convolution with a difference filter (high- pass) and a decimation (3.5.6) Note 1 to entry: The weighting function of the difference filter is defined by the wavelet from a particular family of wavelets, with a particular dilation (3.2.1) parameter and no translation (3.2.2). Note 2 to entry: The filter coefficients require the evaluation of an integral over a continuous space unless there exists a complementary function to form the basis expanding the signal/profile.ISO 16610-29 pdf download.