This is a Demonstration of two-dimensional Lissajous figures of sine-Gaussian waves. You can vary the patterns by changing the frequency and the quality factor in the and directions. The quality factor is the ratio of the frequency to bandwidth; it measures how many cycles there are in the signal in a particular direction.
For a time-frequency search for statistically significant excess signal energy, sine-Gaussians are natural choices as templates. They have the minimum error uncertainty in the time-frequency domain. Such waveforms are sometimes encountered from astrophysical sources. In this Demonstration the shapes of the sine-Gaussian signals are shown for different frequencies and quality factors.