The Fourier transform is not just limited to simple lab examples. When used in real situations it can have far reaching implications about the world around us.

Take for example the field of astronomy. Some times it isn't possible to get all the information you need from a normal telescope and you need to use radio waves or radar instead of light. These radar signals are treated just like any other ordinary time varying voltage signal and can be processed digitally.


One recent example of this technique was the NASA  Magellan satellite which was released from the space shuttle Atlantis on 4th May 1989 and sent to Venus on a 15 month journey that took it one and a half times around the sun.

Venus is Earth's closest planetary companion, and is comparable in its size and diameter. It is difficult to study the surface of Venus because it is perpetually covered with a cloud layer which normal optical telescopes can't penetrate, so Magellan had radar and advanced Digital Signal Processing that was designed to see through this cloud layer. It's mission was map the planet with radar and to reveal surface features as small as 250 meters across.

The black and white pictures that it sent back were strips of the planets surface, about 20 km wide, from the north pole to the south pole. One example image of a surface feature called "Pandora Corona" is shown next. If you look at the image, you will see a two black lines through the picture. This is just a mismatch between the strips sent back by Magellan. It also gives you an idea of the scale of the image as each strip is 20 km wide.

Pandora Corona
From the radar signal received from the planet Magellan was also able to gather other information about the planets surface. The next image is a global map of venus showing emissitivity of the Venus's surface.
Microwave emissitivity of Venus.

By the end of the mission Magellan had far exceeded the mission objectives by mapping 99% of the planet's surface, and by giving unpresidented detail. By piecing all the information together from this mission and from earlier Pioneer-Venus orbiter data, as well as the Soviet Venera 13 and 14 spacecraft, they were able to produce the following mosaic image which is a global view of Venus using simulated color to enhance small scale structures.
Global view of Venus.
Magellan was also carrying another smaller antenna that pointed straight down and measured the time taken for a signal to reflect off the surface. This was used to build up a topographic map of the surface beneath the spacecraft. Combining this data with the earlier radar images they were able to construct a 3D model of the surface of Venus. The model was animated to provide an MPEG movie that flies you across the Maxwell Mountains on Venus. Any of this would have been impossible if it had not been for Digital Signal Processing and the Fast Fourier Transform.
MPEG movie constructed from venus radar data.

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