BS EN ISO 16610-29 pdf free download

BS EN ISO 16610-29 pdf free download. Geometrical product specifications (GPS) — Filtration.
4 General wavelet description 4.1 General A cubic prediction wavelet claiming to conform with this document shall satisfy the procedure given in Annex A. A cubic spline wavelet claiming to conform with this document shall satisfy the procedure given in Annex B. NOTE The relationship to the filtration matrix model is given in Annex C. 4.2 Basic usage of wavelets Wavelet analysis consists of decomposing a profile into a linear combination of wavelets g a,b (x), all generated from a single mother wavelet [4] . This is similar to Fourier analysis, which decomposes a profile into a linear combination of sinewaves, but unlike Fourier analysis, wavelets are finite in both spatial and frequency domain. Therefore, they can identify the location as well as the scale of a feature in a profile. As a result, they can decompose profiles where the small-scale structure in one portion of the profile is unrelated to the structure in a different portion, such as localized changes (i.e. scratches, defects or other irregularities). Wavelets are also ideally suited for non-stationary profiles. Basically, wavelets decompose a profile into building blocks of constant shape, but of different scales. The mother wavelet of the discrete wavelet transform is defined as a set of discrete high-pass filter coefficients, g j , and the scaling function as a set of discrete low-pass filter coefficients, h j . As the decimation is carried out by keeping every second value of the smooth and every second of the difference signal, the total number of data points is conserved, such that n/2 of the s 1 (i) are saved and n/2 of the d 1 (i) and the distance between the i-th and the (i+1)-th is then 2Δx. For the second decomposition step, the set of n/2 differences, d 1 (i), will be kept until termination but the set of the s 1 (i) is subdivided half and half, such that n/4 values s 2 (i) and n/4 values d 2 (i) are obtained. For the k-th step of decomposition and decimation n/2 k of s k (i) and n/2 k values d k (i) are evaluated and the distance between the i-th and the (i+1)-th is then 2 k Δx. Therefore, the dilation is done by down-sampling, i.e. managing the indices of the signal rather than changing the wavelet and scaling functions. Thus, for discrete wavelet transformations only the two sets of filter coefficients, the set {h j , j = −m,..,0,..m} for the low-pass and {g j , j = −m,..,0,..m} for the high- pass, define the analysis filter. 4.4.2 Cubic prediction wavelets A fast implementation of the wavelet decomposition and reconstruction has been employed using a lifting scheme with three stages: splitting, prediction and updating, originally introduced by Sweldens, in which the Neville polynomials are employed to implement the prediction stage by interpolating between sampling positions [6,7] . The cubic prediction wavelets in Annex A using Sweldens’ lifting scheme [6] has been validated as an efficient tool for fast and in-place wavelet transform for geometrical products applications, for example surface metrology [9] . 4.4.3 Cubic b-spline wavelets Spline wavelets are based on the spline function. In this document a cubic b-spline function is used, which has a compact support. The particular cubic spline wavelets used are the biorthogonal wavelets CDF 9/7 with four vanishing moments, detailed in Annex B. This was original introduced by Cohen et al. [8] and has been used in geometrical products applications, for example multiscale analysis. The cubic spline wavelet transform can be implemented using both the Fourier method and the lifting scheme (however, it is a five-stage process) with relevant precision. 5 Filter designation Lifting schemes using cubic interpolation for the wavelet transform in conformity with this document are designated: FPLWCP CDF 9/7 Spline wavelets in conformity with this document are designated: FPLWCS See also ISO 16610-1:2015, Clause 5.BS EN ISO 16610-29 pdf download.