SUMMARY

Designs and applies an adaptive Wiener filter.

SYNTAX

WIENER {[W]INDOW pdw} {[N]COEFF n} {MU OFF | ON | v}
     {[EPS]ILON OFF | ON | e}

INPUT

WINDOW pdw: Set filter design window to pdw. A partial data window which consists of a start time and stop time. These times can be absolute ones or ones relative to certain header fields. See the CUT command for details on pdw.

NCOEFF n: Set the number of filter coefficients to n.

MU off | on | v:

Set the adaptation step size parameter. Off sets mu to zero. On sets mu = 1.95 / Rho(0). Where Rho(0) is the autocorrelation in pdw at zero lag. v sets mu = v.

EPSILON e: Set ridge regression parameter to epsilon. Can help stabilize the wiener filter by increasing the diagonal elements of the autocorrelation matrix by epsilon. When epsilon is ON, SAC will use the value entered by the user (or zero if no value was entered). When epsilon is OFF, SAC will loop through the following increasing values of epsilon (0.0, 1e-5, 1e-4, 1e-3, 1e-2), until the wiener filter is stable, or until the list has been exhausted. If epsilon == 0 does not work, SAC will produce one or more warning messages. If none of the values work, SAC will produce an error message.

WINDOW pdw:	Set filter design window to pdw. A partial data window which consists of a start time and stop time. These times can be absolute ones or ones relative to certain header fields. See the CUT command for details on pdw.
NCOEFF n:	Set the number of filter coefficients to n.
MU off \| on \| v:
	Set the adaptation step size parameter. Off sets mu to zero. On sets mu = 1.95 / Rho(0). Where Rho(0) is the autocorrelation in pdw at zero lag. v sets mu = v.
EPSILON e:	Set ridge regression parameter to epsilon. Can help stabilize the wiener filter by increasing the diagonal elements of the autocorrelation matrix by epsilon. When epsilon is ON, SAC will use the value entered by the user (or zero if no value was entered). When epsilon is OFF, SAC will loop through the following increasing values of epsilon (0.0, 1e-5, 1e-4, 1e-3, 1e-2), until the wiener filter is stable, or until the list has been exhausted. If epsilon == 0 does not work, SAC will produce one or more warning messages. If none of the values work, SAC will produce an error message.

DEFAULT VALUES

WIENER WINDOW B 0 10 NCOEFF 30 MU OFF EPSILON OFF

DESCRIPTION

A prediction error filter is designed using the Yule-Walker Method from an autocorrelation function estimated from the designated partial data window. This window can be any portion of the file. The filter is then applied to the entire signal, i.e. the signal is replaced by the residual error sequence. This filter may be used as a prewhitener or as a detection preprocessor for transient signals. The filter can be made adaptive in time by specifying a non-zero value for MU. Large values of MU may cause instability.

EXAMPLES

The following command would apply a non-adaptive filter, with the first ten seconds being the design window:
SAC> WIENER WINDOW B 0 10 MU 0.
The following command would apply a filter with 40 coefficients, with a design window from the beginning of the file to 1 second before the first arrival:
SAC> WIENER NCOEFF 40 WINDOW B A -1

HEADER CHANGES

DEPMIN, DEPMAX, DEPMEN

ERROR MESSAGES

1301: No data files read in.
1306: Illegal operation on unevenly spaced file
1307: Illegal operation on spectral file
1608: Bad Wiener filter noise window for file
- Filter design window does not lie within file window.
- Make sure header fields used in window are defined.

WARNING MESSAGES

1609: Numerical instability in Wiener filter for file
1614: Numerical instability in Wiener;
- will retry with epsilon = e where e denotes the next value of epsilon to be tried.
- The filtered data may or may not be incorrect.

SEE COMMANDS

CUT

LATEST REVISION

March 12, 1997 (Version 00.53)