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##

Weighting Functions

By default the input signal source is assumed to have a `white' spectrum,
that is, its power spectral density is assumed to be independent of frequency.
It is also assumed that the circuit which is connected to the output
of the filter is equally sensitive to noise at all frequencies.
If this does not represent the actual situation,
assumptions can be modified using an *input and output weighting
function*.

The input weighting function *S*_{i}
is used to determine | *f*_{i}|_{2}^{2}
in (19). Similarly, the output weighting functions *S*_{o}
is used to determine | *g*_{i}|_{2}^{2}
, which is used in (24).
In FA specifications, the input weighting function
is called `si`, and the output weighting
function is `so`. They must directly or indirectly be specified
as a function of frequency, represented by the variable `fr`.
If the input spectrum is expected to be a sinc function it could be
specified like this,

si = (sin(fr * 1000) / (fr * 1000))^2;

or equivalently like this. si = (sin(x) / x)^2;
x = fr * 1000;

For the change to take effect the flag `num` must be set.
If this is done the optimizations and the dynamic range evaluations
will use the weighting functions.

** Next:** Optimization of Dynamic Range
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2009-06-03