Abstract: Wavelet transform becomes a more and more common method of processing 3D signals. It is widely used to analyze data in various branches of science and technology (medicine, seismology, engineering, etc.). In the field of mechanical engineering wavelet transform is usually used to investigate surface micro- and nanotopography. Wavelet transform is commonly regarded as a very good tool to analyze non-stationary signals. However, to analyze periodical signals, most researchers prefer to use well-known methods such as Fourier analysis. In this paper authors make an attempt to prove that wavelet transform can be a useful method to analyze 3D signals that are approximately periodical. As an example of such signal, measurement data of cylindrical workpieces are investigated. The calculations were performed in the MATLAB environment using the Wavelet Toolbox.
B I B L I O G R A F I A[1] Lee, J.-D.(1999). Wavelet Transform for 3-D Reconstruction from Series Sectional Medical Images. Mathematical and Computer Modelling, 30, 1-13.
[2] Jiang, X.Q., Blunt, L. (2001). Morphological assessment of in vivo wear of orthopaedic implants using multiscalar wavelets. Wear, 250, 217-221.
[3] Chen, M., et al. (2008). Analysis of 3D microtopography in machined KDP crystal surfaces based on fractal and wavelet methods. International Journal of Machine Tools & Manufacture, 48, 905-913.
[4] Wang, H.X., et al. (2010). Modification of three dimensional topography of the machined KDP crystal surface using wavelet analysis method. Applied Surface Science, 256, 5061-5068.
[5] Jiang, X.Q., Blunt, L., Stout, K.J. (2001). Application of the lifting wavelet to rough surfaces. Precision Engineering, 25, 83-89.
[6] Jiang, X.Q., Blunt, L. (2004). Third generation wavelet for the extraction of morphological features from micro and nano scalar surfaces. Wear, 257, 1235-1240.
[7] Abdul-Rahman, H.S., Jiang, X.Q., Scott, P.J. (2013). Freeform surface filtering using the lifting wavelet transform. Precision Engineering, 37, 187-202.
[8] Jurko, J., Panda, A., Behún, M. (2012). Analysis of cutting zone machinability during the drilling of XCr18Ni8 stainless steel. Applied Mechanics and Materials, 224, 142-145.
[9] Šolc, M., Markulik, S., Grambalová, E. (2012). Quality of refractory materials in the technological process. Advanced Materials Research, 524-527, 2026-2030.
[10] Adamczak, S., Makieła, W., Stępień, K. (2010). Investigating advantages and disadvantages of the analysis of a geometrical surface structure with the use of Fourier and wavelet transform. Metrol. Meas. Syst., 12(2), 233-244.
[11] Chui, C.K. (1992). An Introduction to Wavelets. Academic Press, New York.
[12] Teolis, A. (1998). Computational Signal Processing with Wavelets. Birkhauser, Boston.
[13] Białasiewicz, J.T. (2004). Wavelets and approximations. 2nd ed. Wydawnictwa Naukowo - Techniczne, Warsaw.
[14] Rak, R.J. (2005). Wavelet analysis of measuring signals. In Proc. of the 7th School-conference ”Computer-aided metrology” . Waplewo, Poland, 9-56.
[15] Makieła, W., Stępień, K. (2010). Evaluation of the methodology of basic wavelet selection on wavelet analysis of surface irregularities. PAK, 1, 32-34.
[16] Brol, S., Grzesik, W. (2009). Continuous wavelet approach to surface profile characterization after finish turning of three different workpiece materials. Advances in Manufacturing Science and Technology, 33(1), 45-57.
[17] Makieła, W. (2008). Decomposition and reconstruction of measurement signals using the wavelet analysis in the Matlab environment. Science Report CEEPUS Project Pl-0007 Geometrical Product Specifications - a new tendency in the design and realization of technological processes, TU Kielce, 117-128.
[18] Zawada-Tomkiewicz, A., Storch, B. (2006). Introduction to the Wavelet Analysis of a Machined Surface Profile. Advances in Manufacturing Science and Technology, 28(2), 91-100.
[19] Zawada-Tomkiewicz, A. (2009). Wavelet decomposition of a surface profiles after turning. PAK, 55(4), 243-246.
[20] Zieliński, T. (2001). Wavelet transform applications in instrumentation and measurement: Tutorial & literature survey. Metrol. Meas. Syst., 5(3), 141-151.
[21] Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.M. (2007). Wavelet Toolbox 4 - User’s Guide The MathWorks, Inc.
[22] Janecki, D., Stępień, K., Adamczak, S. (2010). Problems of measurement of barrel - and saddle-shaped elements using the radial method. Measurement, 43(5), 659-663.
[23] Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41, 909-996.
[24] Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia, USA.
[25] Janecki, D. (2012). Edge elimination effect elimination in the recursive implementation of Gaussian filters. Precision Engineering, 36(1), 128-136.
[26] Janecki, D. (2011). Gaussian filters with profile extrapolation. Precision Engineering, 35(4), 602-606.
[27] Janecki, D. (2009). A generalized L2-spline filter. Measurement, 42(6), 937-943.
[28] Dobrzanski, P., Pawlus, P. (2010). Digital filtering of surface topography: Part II. Applications of robust and valley suppression filters. Precision Engineering, 34, 651-658.
[29] Li, H., et al. (2006). A novel robust Gaussian filtering method for the characterization of surface generation in ultra-precision machining. Precision Engineering, 30, 421-430. 
DOI 
Web of Science 
YADDA/CEON