9827

Aliasing in Time Series Analysis

The relationship between two sinusoidal signals and is shown for and The signals are assumed to be observed at times and the observed points are indicated. When is an integer the points on the curve coincide and the signals are said to be aliased. Considering all frequencies in the range , the largest value of so that all signals may be identified from the observed points is called the Nyquist frequency. It is well known that .

THINGS TO TRY

SNAPSHOTS

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

DETAILS

The spectral density function for a stationary time series , with autocovariance function , can also be written as
.
The sdf can be interpreted as the amount of variability accounted for by a sinusoid with frequency .
Let . Then we can write where is an integer and . Then we see that . Consequently all such frequencies are said to be aliased with . The highest frequency that can be represented in a discrete time series sampled at times is 0.5 and is known as the Nyquist frequency. More generally, if the time interval between observations is Δ then the Nyquist frequency is Δ/2.
    • 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+