Fourier examined at the École Normale in Paris, educated by Lagrange, which Fourier referred to as the very first among European males of scientific research, Laplace, that Fourier rated less extremely, and by Monge. He was appointed to the École Centrale des Travaux Publiques, the college being under the instructions of Carnot and also Monge, which was quickly to be renamed École Polytechnique. In 1807 he amazed several of his contemporary maths wizzard and also researchers by insisting that an arbitrary function could be revealed as a linear combination of sine and cosine features, called Fourier trignometric series, are put on the analysis of periodic phenomena including vibrations and wave movement.
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Jean Baptiste Joseph Fourier
Born: 21 March 1768 in Auxerre,
Bourgogne, France
Died: 16 May 1830 in Paris, France
Point of Fast Fourier Transform
Fast Fourier transform introduced by seismologists.
Rapidly spread to oil industry and more recently to all signal processing, including music.
Direct calculation of DFT required N2 multiplications.
Calculation of FFT requires N log2 N multiplications.
For small sample, e.g. N=4096, DFT requires more than 16 million calculations, while the FFT requires less than 50,000.
So this is the basis of modern digital signal processing.
