Waveform applications of least squares

  By the methods of calculus, one learns to find the coordinates of an extremal point on a curve. In the calculus of variations, one learns how to find extremal functions. In practice, the continuum may be approximated on a mesh and the distinction blurs. In the calculus of variations problems, however, the matrices can be immense, a disadvantage often partially offset by their orderly form. In this chapter we will take up examples in the use of least squares on waveforms and relationships between groups of waveforms. This leads to a massive full matrix called the block-Toeplitz matrix for which we have a special solution technique.