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The Two Century Old Math Trick Behind Our Digital Photos and Videos
Guest Author: Ted Kraver, Ph.D.
Great STEM minds were not all born in the 20th century. Jean Baptiste Joseph Fourier was born in 1768 and orphaned at age 9. Educated by the Benedictines, and surviving the French revolution and Reign of Terror he found himself with returning from Napoleon’s Egyptian expedition in 1801 with an ink pressed copy of the Rosetta Stone. The Rosetta Stone was the key to deciphering Egyptian hieroglyphs by using the Greek and Coptic letters also on the stone. READ MORE.
Fourier was both a mathematician and a physicist. He began by experimenting with the transmission of heat. His innovations include mathematics applied to the physics of heat conduction. The two most important were the use of partial differential equations and dimensional analysis. Determining that a planet the size of the Earth could not be warmed by just the incoming solar radiation, he believed that the atmosphere must be an insulator. This was the first proposal of what we now call the greenhouse effect. His mechanism if heat convection is used today.
He is most famous for the theorem that bears his name, the Fourier Theorem. The theorem states that an infinite series of periodic waves such as Sine waves or Cosine waves can be added together to form any shape whether regular like a triangular wave or irregular like a random squiggle. Circles can also be used. The resulting Fourier Transform is used over a wide range of current applications: voice recognition, optics, radio, animation, music, quantum physics and medical body scans to name a few.
The huge benefit of the Fourier transformation is that it can compress the huge number of data points needed, for instance, to present a digital color photograph into a much smaller data set. The most common picture data set is a JPEG file that comes out of your camera as a photo.jpg. I was attending my wife’s high school class reunion a couple of decades ago and I got to talking with a husband of one of her classmates. It turned out that he had worked for the air force space program when we started sending up spy satellites in the late 1950’s. We needed to send digital photos back to Earth immediately, but did not have the bandwidth capacity in the early days of space flight. His team was responsible for the “crash” effort to create the Fourier techniques to compress the digital images. Their work resulted in JPEG that we all use. The follow on audio/video technology became known as MPEG that produces the MP3’s we enjoy.
Not a bad set of accomplishments for a poor orphan from the city of Auxerre, France.
http://tinyurl.com/FourierAndHomer For a demo of how JPEG works.
http://tinyurl.com/blogMathTrick-for-JPEG-MPEG For a more complete description of Fourier techniques.