Equation (3) shows an example
where the first output signal is the ordinary one
and the second output signal used a filter interlaced with zeros.
We prepare subroutines that allow for more output signals,
each with its own filter interlace parameter
given in the table `jump(ns)`.
Each entry in the jump table corresponds to
a particular scaling of a filter axis.
The number of output signals is `ns` and the
number of zeros interlaced between filter points
for the `j`-th signal is `jump(j)-1`.

The multiscale helix filter is defined in module
`mshelix` , analogous to the
single-scale module `helix` .
A new function
`onescale`
extracts our usual helix filter
of one particular scale
from the multiscale filter.
mshelixmultiscale helix filter definition
We create a multscale helix with module
`createmshelixmod` .
An expanded scale helix filter is like an ordinary helix filter
except that the lags are scaled according to a `jump`.
createmshelixmodcreate multiscale helix

First we examine code for estimating a prediction-error filter
that is applicable at many scales.
We simply invoke the usual filter operator
`hconest`
for each scale.
mshconestmultiscale convolution, adjoint is the filter
filter ! multiscale prediction-error

The multiscale prediction-error filter finding subroutine
is nearly identical to the usual subroutine
`find_pef()` .
(That routine cleverly ignores missing data while estimating a PEF.)
To easily extend `pef` to multiscale filters
we replace its call to the ordinary helix
filter module
`hconest`
by a call to `mshconest`.
mspefmultiscale PEF
The purpose of `pack(dd,.true.)`
is to produce the one-dimensional array expected by
our solver routines.

Similar code applies to
the operator in
(4)
which is needed for missing data problems.
This is like
`mshconest`
except the adjoint is not the filter but the input.
msheliconmultiscale convolution, adjoint is the input
The multiscale missing-data module `msmis2`
is just like the usual missing-data module
`mis2`
except that
the filtering is done with the multiscale filter
`mshelicon` .
msmis2multiscale missing data

4/27/2004