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Jean Baptiste Joseph Fourier, a great mathematician, was born in 1768, Auxerre, France. His special interest in heat conduction led him to describe a mathematical series of sine and cosine terms that could be used to analyze propagation and diffusion of heat in solid bodies. In 1807, he tried to share his innovative ideas with researchers by preparing an essay entitled as On the Propagation of Heat in Solid Bodies. The work was examined by Lagrange, Laplace, Monge, and Lacroix. Lagrange's oppositions caused the rejection of Fourier's paper. This unfortunate decision cost colleagues to wait for 15 more years to meet his remarkable contributions to mathematics, physics, and especially on signal analysis. Finally, his ideas were published thru the book The Analytic Theory of Heat in 1822 (Fourier 1955).

Discrete Fourier transform (DFT) was developed as an effective tool in calculating this transformation. However, computing FT with this tool in the nineteenth century was taking a long time. In 1903, C. Runge has studied on the minimization of the computational time of the transformation operation (Runge 1903). In 1942, Danielson and Lanczos had utilized the symmetry properties of FT to reduce the number of operations in DFT (Danielson and Lanczos 1942). Before the advent of digital computing technologies, James W. Cooley and John W. Tukey developed a fast method to reduce the computation time of DFT operation. In 1965, they published their technique that later on has become famous as the fast Fourier transform (FFT) (Cooley and Tukey 1965).