Frequency decomposition of images

We have seen that psychoacoustics provides a compelling motivation for decomposing audio signals as sums of sinusoids. In principal, images can also be similarly decomposed. However, the motivations in this case are more mathematical than human. The following applet illustrates sinsoidal images: If you were able to run applets, you would have an applet here.

The image is sinusoidal. The checkboxes at the right control whether a vertical sinusoid, a horizontal sinusoid, both, or neither is shown. The scrollbars control the vertical and horizontal periods.

These images have much less meaning than audio sinusoids, which we perceive as musical tones. Nonetheless, we will see that images can be described as sums of sinusoids, and that such description is sometimes useful.