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Equation (4) is a frequency-domain quadratic form
that we minimized by varying a single parameter,
a Fourier coefficient.
Now we will look at the same problem in the time domain.
We will see that the time domain offers flexibility with
boundary conditions, constraints, and weighting functions.
The notation will be that a filter ft has input xt and output yt.
In Fourier space this is Y=XF.
There are two problems to look at,
unknown filter F and unknown input X.