PS;
The Fast Fourier Transform (FFT), has become well known as a very efficient algorithm for calculating the Discrete Fourier Transform (DFT). The DFT is used in many disciplines to obtain the spectrum or frequency content of a Signal, and to facilitate the computation of discrete convolution and correlation.
The FFT algorithm as a means of calculating the DFT, by J. W. Cooley and J. W. Tukey in 1965, was a turning point in DSP and in numerical analysis. They showed that the DFT, which was previously thought to require N^2 arithmetic operations, could be calculated by the new FFT algorithm using only N ln N operations.
BUT later surfaced historical documents showed that this was really been found by Carl Friedrich Gauss, the eminent German mathematician. He had an algorithm similar to the FFT for the computation of the coefficients of a finite Fourier series. Gauss' treatise describing the algorithm was not published in his lifetime; it appeared only in his collected works as an unpublished manuscript. The presumed year of the composition of this treatise is 1805. It even predates Fourier's 1807 work on harmonic analysis.
Thus it took another 160 years after Gauss for someone else to re-invent it.
