9772

Transfer Function from Poles and Zeroes

Build a transfer function out of a collection of poles (in red) and zeroes (in blue) in the complex plane. When poles and zeroes are complex conjugates, the amplitude of the transfer function is symmetric and the phase is antisymmetric, which corresponds to a real impulse response. Otherwise, the impulse response is complex.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshot 1: A single zero in creates a high-pass filter, since the amplitude term (in blue, top-right graph) shows attenuation near the origin. The phase term (in purple, bottom-right graph) is linear but has a discontinuity at the origin.
Snapshot 2: This filter has lowpass characteristics. It has a real impulse response since the poles and zeroes are symmetric. The attenuation is good, but there are strong ripples in the pass-band.
Snapshot 3: This filter is characterized by symmetric zeroes but asymmetric poles; therefore, its impulse response is complex. This can also be observed from its phase, which does not satisfy Hermitian symmetry, nor does the amplitude.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+