Exploratories

Description

The key to understanding aliasing and what we do about it is the Nyquist limit. The Nyquist limit gives us a theoretical limit to what rate we have to sample a signal that contains data at a certain maximum frequency. Once we sample below that limit, not only can we not accurately sample the signal, but the data we get out has corrupting artifacts. These artifacts are "aliases".

Students can set the frequency of a sine wave which is sampled into a discrete signal and then reconstructed back into a continuous one. The can also control the sampling rate. When the sampling rate is high enough, a good reconstruction of the original signal emerges. When it is too low, however, the results clearly go haywire, demonstrating the Nyquist limit.

Aliases are so named because when a signal is sampled below the Nyquist limit, high-frequency inputs can masquerade as lower-frequency

outputs. At certain settings of the input frequency and sampling rate, this effect can clearly be seen by students.

Audience

Students interested in the nyquist limit and how it relates to aliasing artifacts in computer graphics and other forms of signal processing.

Usage

Adjust the frequency of the sine wave to be sampled as well as the sampling frequency by using the sliders located under the topmost graphing window in the applet. As you adjust the rate at which you sample the sine wave, see what happens to the reconstructed signal. Try setting the sampling rate to be low and then vary the frequency to see the low-frequency aliases of the input signal.

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