From Oppenheim & Willsky, Interpolation is a commonly used procedure for reconstructing a function, either approximately or exactly, from samples. More so, interpolation is the fitting of a continuous signal to a set of sample values. Interpolation can also be defined as a specific form of curve fitting where the curve must pass directly through the points.
Professor Mimi showed us 0th-order interpolation (Piecewise constant) and 1st-order interpolation (splines). These are not the only types of interpolation.
According to Wikipedia, other forms of interpolation include linear and polynomial.
Linear Interpolation
Linear interpolation compares two points and applies "connect the dots."
Given two points (X1,Y1) and (X2,Y2):
$ Y_n = Y_1 + \frac{(X_n-X_1)(Y_2-Y_1)}{(X_2-X_1)} $
Polynomial Interpolation
Polynomial interpolation uses the concept of linear interpolation except for the fact that a polynomials of higher orders are used. Polynomials should increase the accuracy of the interpolation, but the cost of calculating such an interpolation is rather high.
