Least-squares estimators

If you are sampling a noisy signal and would like to extract information from those samples, the ideal tool is to use least-squares polynomials; however, this requires one to generate and solve the normal equation $A^T Ac = A^T{\bf y}$, and operation that is relatively expensive for a real-time system.

Instead, if the data is periodically sampled, then the equal spacing between the samples simplifies the formulas so that many of the estimators can be found using nothing more than a linear combination of the sampled values. This reduces the run-time significantly.

The paper least-squares estimators on periodically sampled noisy signals describes this technique, and the source directory contains an executable that will print out the coefficients.