{"title":"Peakwise Smoothing of Data Models using Wavelets","authors":"D Sudheer Reddy, N Gopal Reddy, P V Radhadevi, J Saibaba, Geeta Varadan","volume":39,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":638,"pagesEnd":644,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/7538","abstract":"Smoothing or filtering of data is first preprocessing step\r\nfor noise suppression in many applications involving data analysis.\r\nMoving average is the most popular method of smoothing the data,\r\ngeneralization of this led to the development of Savitzky-Golay filter.\r\nMany window smoothing methods were developed by convolving\r\nthe data with different window functions for different applications;\r\nmost widely used window functions are Gaussian or Kaiser. Function\r\napproximation of the data by polynomial regression or Fourier\r\nexpansion or wavelet expansion also gives a smoothed data. Wavelets\r\nalso smooth the data to great extent by thresholding the wavelet\r\ncoefficients. Almost all smoothing methods destroys the peaks and\r\nflatten them when the support of the window is increased. In certain\r\napplications it is desirable to retain peaks while smoothing the data\r\nas much as possible. In this paper we present a methodology called\r\nas peak-wise smoothing that will smooth the data to any desired level\r\nwithout losing the major peak features.","references":"[1] Edward. A. Bender, An Introduction to mathematical modeling, 1978,\r\nJohn Wiley and Sons Inc.\r\n[2] William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P.\r\nFlannery,Numerical Recipes, 3ed. Cambridge University Press, 2007.\r\n[3] Jeffrey. S.Simonoff, Smoothing methods in statistics, Springer Verlag,\r\nNew York, 1996.\r\n[4] Savitzky A, Golay MJE, Smoothing and differentiation of data by\r\nsimplified least squares procedures. Analytical Chemistry 1964, 36:1627-\r\n1639.\r\n[5] Peter A Gorry, General Least-Squares Smoothing and Differentiation by\r\nthe Convolution (Savitzky-Golay) Method. Analytical Chemistry, 1990,\r\n62, pp 570-573.\r\n[6] Hamming. R.W., Digital Filters, Prentice Hall Signal Processing Series,\r\n3ed, 1989.\r\n[7] Fredric J Harris, On the Use of Windows for Harmonic Analysis with\r\nthe Discrete Fourier Transform, Proceedings of the IEEE, Vol 66, No. 1.\r\nJanuary 1978.\r\n[8] Mallat.S, A Wavelet Tour of Signal Processing, 2 ed. San Diego, CA:\r\nAcademic, 1999.\r\n[9] Mallat. S., Wen Liang Hwang, Singularity Detection and processing with\r\nwavelets, IEEE Trans. on Information Theory, vol. 38, No. 2, March 1992.\r\n[10] Orbital Debris Quarterly News, Vol. 14, Issue-3.\r\n[11] Klinkrad, H., Space Debris, Models and Risk Analysis, Springer-Praxis\r\nPublishing, 2006.\r\n[12] Ananthasayanam, M. R., Anilkumar, A. K., and SubbaRao, P. V., 2006,\r\nStochastic impressionistic Low Earth Model of the space debris scenario,\r\nACTA Astronautica, Vol. 59, pp. 547-559.\r\n[13] Anilkumar, A. K., Sudheer Reddy. D., Statistical conjunctiona analysis\r\nof LEO catalogued objects, Journal of Spacecraft and Rockets, AIAA,\r\npp. 160-167, Jan-Feb 2009.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 39, 2010"}