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Statistics

  

LinearFilter

  

apply linear filter to a data set

 

Calling Sequence

Parameters

Description

Options

Examples

Calling Sequence

LinearFilter(X, Y, options)

Parameters

X

-

data set

Y

-

filter

options

-

(optional) equation(s) of the form option=value where option is one of ignore or initial; specify options for the LinearFilter function

Description

• 

The LinearFilter function applies linear filter to a set of observations. By default, convolution method is used:

`X'`[i] = Sum(X[i+1-j]*Y[j], j = 1..m);

X'i=j=1mXi+1jYj

(1)
  

where m is the size of the filter. For i<m the set of initial values will be used. By default, X is padded on the left with m1 zeros. Option initial can be used to specify the initial values.

  

Recursive filter is defined as follows:

`X'`[i] = X[i]*Y[1]+Sum(`X'`[i+1-j]*Y[j], j = 2..m);

X'i&equals;XiY1&plus;j&equals;2mX'i&plus;1jYj

(2)
• 

The first parameter X is a single data sample - given as e.g. a Vector. Each value represents an individual observation.

• 

The second parameter Y is the filter - given as e.g. a Vector. Each value represents a filter coefficient.

Options

  

The options argument can contain one or more of the options shown below.

• 

ignore=truefalse -- This option is used to specify how to handle non-numeric data. If ignore is set to true all non-numeric items in data will be ignored. Missing values are allowed in the data set but not in the filter.

• 

initial=deduce, or Vector -- This option specifies the initial values in reverse order. The default is a set of m1 zeros.

• 

recursive=truefalse -- If this option is set to true then recursive filter will be used.

Examples

withStatistics&colon;

Aseqsini&comma;i&equals;1..9&comma;undefined&colon;

LinearFilterA&comma;1.&comma;0.3&comma;0.2

0.8414709848078971.161738722268050.5822034330691510.5326070075248321.157741021643540.7184532796594530.3813770943264841.130571126599230.840323278972529HFloatundefined

(3)

LinearFilterA&comma;1.&comma;0.3&comma;0.2&comma;ignore

0.8414709848078971.161738722268050.5822034330691510.5326070075248321.157741021643540.7184532796594530.3813770943264841.130571126599230.840323278972529

(4)

LinearFilterA&comma;1.&comma;0.3&comma;0.2&comma;ignore&comma;initial&equals;3&comma;2&comma;1

2.141470984807901.761738722268050.5822034330691510.5326070075248321.157741021643540.7184532796594530.3813770943264841.130571126599230.840323278972529

(5)

LinearFilterA&comma;1.&comma;0.3&comma;0.2&comma;ignore&comma;recursive

0.8414709848078971.161738722268050.6579358217018620.3270740043437600.9254593116258940.6224680925554460.2851543086269760.9504109207003850.754272623177268

(6)

See Also

Statistics

Statistics[DataSmoothing]

Statistics[ExponentialSmoothing]

 


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