Separable and Nonseparable 2D Sequences

This Demonstration shows a separable 2D sinusoidal sequence (left) versus the nonseparable one (right) displayed as 16×16 images, with heights represented by colors.
where and are horizontal and vertical directions, respectively, and and are the horizontal and vertical angular frequencies. This sequence is called separable because it is obtained as a product of two one-dimensional sequences. Thus, if any of the sliders are set to 0, the sequences will be 0 (constant image). For any combinations of sliders, the resulting pattern will be rectangular.
The right figure (nonseparable) is generated using
This sequence is called nonseparable because it cannot be obtained as a product of two one-dimensional sequences. If one of the sliders is set to 0 and the other to any nonzero value, the resulting image will show a pattern only in one dimension. If both sliders are set to a nonzero value, the resulting pattern will never be rectangular.
The fact that the separable sequence can only achieve rectangular space patterns, while the nonseparable one offers more flexibility, is often used in discrete-time signal processing to design filters.


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


[1] M. Vetterli, J. Kovačević, and V. K. Goyal, Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014. www.fourierandwavelets.org.
    • 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+