# rootFilter(a,zeroes,poles)

Implements an analog filter with transfer response specified by poles and zeroes.

### Syntax

o_rootFilter(a,zeroes,poles)
  a: Waveform or Spectrum - inputSignal
  zeroes: array 1D Complex - zeroes of numerator polynomial
  poles: array 1D Complex - zeroes of denominator polynomial
  return: Waveform or Spectrum - output signal formed by passing through defined filter

### Usage

Analog filters are generally specified by a rational polynomial. Use this filter when you know the roots (zeroes and poles) of the defining polynomial.

### Location

menu: veeos ==> Signal Processing ==> Modules ==> rootFilter

library: sigLib

### Example

see example in veeos menu

### Notes

In general a linear (analog) filter may be defined by the rational polynomial H(S) where Output(S)=Input(S)*H(S). A typical H(S) rational polynomial may be expressed as:
( (S-z[0])*(S-z[1])*...(S-z[i]) ) / ( (S-p[0])*(S-p[1])*...(S-p[i]) )

where z and p are the roots of the numerator and denominator polynomials. This function inputs those two vectors, determines H(jF), and filters the input signal appropriately.

If you have a zeroes at infinity then the numerator will be just a constant. In this case you may be better off using polyFilter. However, perhaps you really do want to work with the poles separately, in which case you can still proceed by noting that the polynomial has factors of the form (S-z[0]) and that you are free to specify anything you like for z[0]. In this case you can, for instance, choose z[0] = "S-67" so that S-z[0] becomes S-S+67 or just 67.

### Reference

### Dependencies

### Supported On

VEE 7.0+, all platforms

### See Also

aFilter, AnalogFilter, funcFilter, rootFilter

© 2015-2021. All Rights Reserved. Stan Bischof (stan@worldbadminton.com). Last updated 09 August 2021 18:25.