10217

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.

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.

PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.