Where data fitting uses
the notation
,
linear algebra and signal analysis often use
the notation
.
Equation (4) is a frequency-domain quadratic form
that we minimized by varying a single parameter,
a Fourier coefficient.
Now, we look at the same problem in the time domain.
We see that the time domain offers flexibility with
boundary conditions, constraints, and weighting functions.
The notation is that a filter has input and output .
In Fourier space, it is expressed .
There are two applications to look at,
unknown filter and unknown input .