RecurrenceFilter

RecurrenceFilter[{α,β},x]
filters x using a linear recurrence equation with coefficients α and β.

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.

RecurrenceFilter[,image]
filters image.

RecurrenceFilter[,sound]
filters sampled sound object.

Details and OptionsDetails and Options

  • RecurrenceFilter[{α,β},x] gives the response y to the input x by solving the recurrence equation for n from to Length[x], where i is Length[α] and j is Length[β].
  • RecurrenceFilter[{α,β},x] uses an initial condition .
  • RecurrenceFilter[{α,β},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 α and β 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 arbitrary-rank numerical arrays, 2D and 3D images, and sampled sound objects, operating separately on each channel.
  • Possible sound objects include:
  • SampledSoundList[{a1,a2,},r]amplitude levels given in a list
    SampledSoundFunction[f,n,r]amplitude levels generated by a function
    Sound[prims,]excluding SoundNote objects in prims
  • 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.
Introduced in 2012
(9.0)
| Updated in 2014
(10.0)