Ideal Nth-Band Discrete Filters

This Demonstration shows impulse and magnitude responses of ideal -band lowpass discrete filters for . While such filters are not realizable in practice, they serve as a desired template for passing certain frequencies while blocking others. The impulse response of an ideal lowpass filter is a sinc sequence (of unit norm in the figure), while its magnitude response is constant in the passband.


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


An ideal -band discrete filter is a non-realizable filter whose magnitude response takes a single nonzero value in its passband. For example, an ideal lowpass filter passes frequencies below some cut-off frequency and blocks the others; its passband is thus the interval .
The impulse response of an ideal lowpass -band filter is a sinc sequence; its unit-norm version is
for .
The impulse response at is thus (see figure).
The magnitude response of a unit-norm is (see figure)
for , and 0 otherwise.
[1] M. Vetterli, J. Kovačević, and V. K. Goyal, Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014. www.fourierandwavelets.org.
[2] Wikipedia. "Sinc Filter." (Nov 10, 2014) en.wikipedia.org/wiki/Sinc_filter.
    • 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.

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 © 2018 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+