9464

Filtering a White-Noise Sequence

This Demonstration creates a white-noise sequence and then uses a low-pass filter to produce a red-noise sequence. The "filter cut-off" is the fractional point in [0, 1] on the spectral frequency axis to apply the filter, as measured from zero frequency. The rate of suppression of frequencies larger than the filter cut-off is given by the "filter roll-off" exponent (1 to 4); larger values of mean greater suppression of the higher frequencies. A new time sequence is generated with the "randomize" button. The amplitude spectrum of the time series is plotted simultaneously, with spectral values on a log scale, out to the Nyquist frequency.

SNAPSHOTS

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

DETAILS

The "white-noise" time sequence is created by sampling from a random normal density. To apply low-pass filtering, the sequence is converted to the frequency domain by a Fourier transform. Then the filtering factor applied to all frequencies in the spectral domain is
,
where is the cut-off frequency and is the roll-off exponent. Note that the factor is always unity at . The filtered Fourier spectrum is then converted back to the time domain by the inverse Fourier transform. The resultant time sequence is commonly called a "red-noise" time sequence.
    • 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.
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+