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Cubic Spline Interpolation versus Interpolating Polynomial

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examples when an interpolating polynomial does well
number of samples
7
signal frequency Hz
1
signal phase
0
cos(π t)
interpolating polynomial
interpolating points
cubic spline
interpolating polynomial
Given
n
equally spaced sample values of a function
f:
, one can approximate
f(t)
as the polynomial of degree
n-1
that passes through all
n
points on a plot. Runge's phenomenon tells us that such an approximation often has large oscillations near the ends of the interpolating interval. On the other hand, cubic spline interpolation is often considered a better approximation method because it is not prone to such oscillations. However, if the sample rate is sufficiently high relative to highest frequency in the signal, then an interpolating polynomial has a smaller approximation error than a cubic spline interpolation.
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