Issue 50

A. Kostina et alii, Frattura ed Integrità Strutturale, 50 (2019) 667-683; DOI: 10.3221/IGF-ESIS.50.57 680 The resulting Savitzky-Golay filter can be written in the following form:            0 M m M C i b m z i m (26) where    0 b is the steady-state (middle) Savitzky-Golay filter obtained by a minimization of the error (25). The optimal values of the half-width of the approximation interval M and the degree of polynomial N for smoothing of the signal presented in Fig. 11 (a) are equal to 8 and 1 respectively. Results of the filtration are presented in Fig. 14 (c). The median smoothing is a non-linear filtering technique [26] which provides an output signal in the following form:              1 2 1 2 2 , 2 1 , 2 2 M M M z M k C i z z M k (27) where 1 z , 2 z , …, M z are the sorted data points in the observation window of the length M . For the considered signal the optimal parameters of the window is 41. The obtained results are given in Fig. 14 (d). (a) (b) (c) (d) Figure 14 : Application of various filtration techniques to the detection of the 8 mm defect located at the depth of 0.6 mm (1 – reconstructed signal, 2 – reference signal, 3 – initial signal with noise): (a) simple moving average, (b) Gaussian filter, (c) Savitzky- Golay filter, (d) median filter.