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s) Gauss and the Fast Fourier Transform

s) Gauss and the Fast Fourier Transform

25.03.2019

 

In 1805, Gauss was trying to compute asteroid orbits from observations of their positions. Rather than solving a system of equations by hand, he looked for a shortcut. He discovered how to split the equations into subproblems that were easier to solve, and then how to recombine the solutions. In essence, he computed the discrete Fourier series of the data with the splitting technique that forms the basis of modern FFT algorithms. His work was published posthumously in 1866 and lay dormant for a century. In 1965, Cooley and Tukey published a modern version of the algorithm and revolutionized digital signal processing. The FFT dramatically speeds up discrete Fourier transformations that are at the core of today's data compression, processing and communication. FFT-based OFDM (Orthogonal Frequency Division Multiplexing), in particular, is today's preferred choice for wireless communication, digital broadcasting, and DSL.

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