Piecewise cubic spline interpolation

This section provides a discussion of piecewise cubic spline interpolation methodology and its application to the term stmcture. Our intent is to provide an accessible approach to cubic spline interpolation for... 

Fig. 4. (A) Parametrization of a shaped pulse envelope with the help of a cubic spline interpolation between a small number of anchor points (circles). (B) Approximation of the smooth pulse envelope by rectangular pulses with piecewise constant rf amplitude. (Adapted from Ewing et al., 1990, p. 123, with kind permission from Elsevier Science—NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The linear algebraic system consists of 3n - 3 equations and 3n - 3 unknowns that can be solved to produce the optimal piecewise cubic spline. Press, Teukolsky, Vetterling, and Flannery describe a routine for cubic spline interpolation. " ... 

MATLAB has several functions for interpolation. The function = interpl(x, y, x) takes the values of the independent variable x and the dependent variable y (base points) and does the one-dimensional interpolation based on x, to find yj. The default method of interpolation is linear. However, the user can choose the method of interpolation in the fourth input argument from nearest (nearest neighbor interpolation), linear (linear interpolation), spline (cubic spline interpolation), and cubic (cubic inteipolation). If the vector of independent variable is not equally spaced, the function interplq may be used instead. It is faster than interpl because it does not check the input arguments. MATLAB also has the function sp/ine to perform one-dimensional interpolation by cubic. splines, using nat-a- not method, ft can also return coefficients of piecewise poiynomiais, if required. The functions interp2, inte.rp3, and interpn perform two-, three-, and n-dimensional interpolation, respectively. 

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