Educational > Applied Maths

Mathematics and the Modern World Changing Words, Sound, and Pictures into Number

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Mohammad Hassan Murad:
Pictures, sound, and text are routinely transmitted from one place to another via the Internet, fax machines, or modems. How can such things be transmitted through telephone wires? The key to doing this is to change them into numbers or bits (the digits 0 or 1). It’s easy to see how to change text to numbers. For example, we could use the correspondence
A = 00000001, B = 00000010, C = 00000011, D = 00000100, E = 00000101,
and so on. The word “BED” then becomes
000000100000010100000100.
By reading the digits in groups of eight, it is possible to translate this number back to the word “BED.”

     Changing sound to bits is more complicated. A sound wave can be graphed on an oscilloscope or a computer. The graph is then broken down mathematically into simpler components corresponding to the different frequencies of the original sound. (A branch of mathematics called Fourier analysis is used here.) The intensity of each component is a number, and the original sound can be reconstructed from these numbers. For example, music is stored on a CD as a sequence of bits; it may look like 101010001010010100101010 10000010 11110101000101011.... (One second of music requires 1.5 million bits!) The CD player reconstructs the music from the numbers on the CD.

    Changing pictures into numbers involves expressing the color and brightness of each dot (or pixel) into a number. This is done very efficiently using a branch of mathematics called wavelet theory. The FBI uses wavelets as a compact way to store the millions of fingerprints they need on file.

Saba Fatema:
Nice & interesting post.

Masuma Parvin:
Very interesting and informative post.

msu_math:
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have specific properties that make them useful for signal processing. Wavelets can be combined, using a "reverse, shift, multiply and sum" technique called convolution, with portions of a known signal to extract information from the unknown signal.

For more detailed visit http://en.wikipedia.org/wiki/Wavelet.

mosfiqur.ns:
 8)

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