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 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.
New in 9
New to Mathematica? Find your learning path »
Have a question? Ask support »