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 OptionsDetails 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 , 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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Filtering of a unit impulse sequence:

 Out[1]=

Filtering of an image:

 Out[1]=