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BUILT-IN MATHEMATICA SYMBOL
RecurrenceFilter
RecurrenceFilter[{
, 
}, x]
filters x using a linear recurrence equation with coefficients and .
RecurrenceFilter[tf, x]
uses a discrete-time filter defined by the TransferFunctionModel tf.
RecurrenceFilter[..., x, {y0, y1, ...}]
uses a specified list 
as the initial condition.
Details and Options
- RecurrenceFilter[{, }, x] gives the response y to the input x by solving the recurrence equation
for n from 
to Length[x], where i is Length[] and j is Length[]. - RecurrenceFilter[{, }, x] uses an initial condition
. - RecurrenceFilter[{, }, x] pads the input x so that
. The values can be changed with the Padding option. »With Padding->None, the response y effectively starts at 
, and the output dimensions are normally smaller than the input. - The specified coefficients and are respectively the denominator and numerator polynomial coefficients of the desired transfer function model.
- In RecurrenceFilter[tf, ...], tf should be a single-input single-output (SISO) system.
- RecurrenceFilter works with arrays of any rank and SampledSoundList objects, as well as 2D and 3D images.
- When applied to images and multidimensional arrays, the specified filter is applied successively to each dimension, starting at level 1.
- For multichannel image and sound objects, RecurrenceFilter is applied to each channel separately.
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