Least-Squares Smoother

Smooths Noisy Data by Minimizing a Cost Function

LSSMOOTH solves an overdetermined system of equations to minimize a combination of output-input squared error and squared high-order derivative in the output. The idea of minimizing this cost function is credited to ID:48799. In LSSMOOTH, the solution method and user controls are different, for numerics and convenience, and with some cost in speed. A companion smoother IRLSSMOOTH (ID:49788) takes this smoothing approach one step farther.

The user specifies the smoother response time in units of samples, which translates to roughly the same bandwidth as a moving average of that many samples. The output is much smoother though, due to greater high-frequency attenuation.

Optionally, the user can specify the highest derivative not to penalize, which affects the smoother's transient response. The default is 2. Lower numbers produce more damping and higher numbers less. In practice the differences are usually subtle. More details about the inputs are found in the code header.

A rare and nice feature of this smoothing approach is that the question of how to treat the ends of the sequence never arises. Every output sample is part of the vector solution to the cost minimization.

See also IRLSSMOOTH, ID:49788