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EEE 244-7: Curve Fitting Need for curve fitting • Engineering projects involve collection of data, such as line voltage, cellular signal power • Curve fitting provides a smooth fit to the data by an approximating function • Data can be approximated by polynomial functions and splines Polynomial functions • Approximating curve yc represented by an mth order polynomial: • Polynomial coefficients c1, c2 ……cm+1 values are obtained from data points • Linear or straight line fit: m = 1 Nonlinear fit : m > 1 3 Matlab functions for polynomial curve fitting • The coefficient matrix C = [c1, c2 ……cm+1] can be calculated by the Matlab polyfit command: C = polyfit(x,y,m) where [x y] is the data set m is the order of the polynomial • The command polyval (C,x0) gives the value of the polynomial at the point x0 4 Example of polynomial curve fitting 5 Cubic splines • Polynomial approximation can produce points that are not allowed • For example, if the data is for absolute voltage, polynomial can have negative and positive values • Splines are piecewise approximating cubic functions that can overcome polynomial problems 6 Matlab command for cubic splines • The Matlab command interp1 creates cubic spline set • Given the data set [x y], the command: yi = interp1(x,y,xi, spline) yields the value of the function at the point xi • The function can be obtained by giving a range of [xi yi[ 7 Example of curve fitting Given the following data set: Write a Matlab program to fit a curve using: • Polynomial function of order 3 • Cubic spline fit In both cases, sketch the approximating function 8