Variable mode averager

DETAILED DESCRIPTION A common smoothing technique uses an average to fit a constant, v.
sup.
A, to a set of data values, {v.
sub.
i ; i=1, 2, .
.
.
, n}: ##EQU1## A generalized form of equation (1) is the weighted average ##EQU2## Here, each value, v.
sub.
i, is scaled by a weight, w.
sub.
i, before averaging.
This allows data values to be emphasized and de-emphasized relative to each other.
If the data relates to an input signal, for example, values occurring during periods of low signal confidence can be given a lower weight and values occurring during periods of high signal confidence can be given a higher weight.
FIG.
2A illustrates the output of a constant mode averager, which utilizes the weighted average of equation (2) to process a discrete input signal, {v.
sub.
i ; i an integer} 110.
The input signal 110 may be, for example, a desired signal corrupted by noise or a signal having superfluous features.
The constant mode averager suppresses the noise and unwanted features, as described with respect to FIG.
5, below.
A first time-window 132 defines a first set, {v.
sub.
i ; i=1, 2, .
.
.
, n}, of signal values, which are averaged together to produce a first output value, z.
sub.
1 122.
A second time-window 134, shifted from the previous window 132, defines a second set {v.
sub.
i ; i=2, 3, .
.
.
, n+1}of signal values, which are also averaged together to produce a second output value z.
sub.
2 124.
In this manner, a discrete output signal, {z.
sub.
j ; j an integer} 120 is generated from a moving weighted average of a discrete input signal {v.
sub.
i ; i an integer} 110, where: ##EQU3## A common filtering technique computes a linear fit to a set of data values, {v.
sub.
i ; i=1, 2, .
.
.
, n}: v.
sub.
i =.
alpha.
.
multidot.
t.
sub.
i +.
beta.
(4) where .
alpha.
and .
beta.
are constants and t.
sub.
i is the time of occurrence of the i.
sup.
th value.
FIG.
2B illustrates the output of a linear mode averager, which uses the linear fit of equation (4) to process a discrete input signal, {v.
sub.
i ; i an integer} 110.
The input signal 110 may be, for example, a desired signal with important features corrupted by noise