Abstract：Fractional spline theory is proposed as a new profile filter for mean line extraction. First, the fractional spline filter is derived by combining fractional spline function with variational principle. The amplitude transmission characteristics of this filter show its adjustability of cut-off characteristics, which can approach ideal low pass filter when the order of spline increases enough, and approximate to Gaussian filter when order is defined 1.51. A fast FFT algorithm is given to perform fractional spline filter. Provided with the limited number of multiplication operation during frequency domain, the computation is testified efficient. Finally, the reasons of end distortion during this algorithm are discussed, and this distortion called end effect is remedied. Experimental results indicate this filter algorithm preserves not only adjustable cut-off characteristics, but also fast computation speed. Based on this filter, once extraction for mean line of 11200 data points only costs 4 ms on general computer. In addition, the end effect existing in spline filter is alleviated by this algorithm availably.
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2011, Vol. 32 
