Spatial aliasing and scale invariance |

Large objects often resemble small objects.
To express this idea we use * axis scaling*
and we apply it to the basic theory
of prediction-error filter (PEF) fitting
and missing-data estimation.

Equations (3) and (4) compute the same thing
by two different methods,
and
.
When it is viewed as fitting goals minimizing
and used along with suitable constraints,
(3) leads to finding filters and **spectra**,
while
(4) leads to finding **missing data**.

A new concept embedded in (3) and (4)
is that one filter can be applicable for different **stretching**s
of the filter's time axis.
One wonders,
``Of all classes of filters,
what subset remains appropriate for stretchings of the axes?''

- Examples of scale-invariant filtering
- Scale-invariance introduces more fitting equations
- Coding the multiscale filter operator

Spatial aliasing and scale invariance |

2013-07-26