The CooleyÂ–Tukey algorithm implements an efficient version of an operation named after this man; the basic form of that operation uses an integral from negative infinity to infinity and contains the term " e  to the minus 2 pi  IVT .
A generalization of one of this man's namesake objects uses a linear combination of orthogonal versions of a Bessel function to solve PDEs in cylindrical coordinates. The CooleyÂ–Tukey algorithm implements an efficient version of an operation named after this man; the basic form of that operation uses an integral from negative infinity to infinity and contains the term " e  to the minus 2 pi  IVT ." This man's most famous mathematical invention may have coefficients of "4 over  n  pi" for odd  n , and zero for even  n , and that (*)  expansion decomposes a periodic function into a sum of trigonometric functions, particularly sines and cosines. For 10 points, name this French mathematician, namesake of a transform and series that analyze signals in the time and frequency domains.
A generalization of one of this man's namesake objects uses a linear combination of orthogonal versions of a Bessel function to solve PDEs in cylindrical coordinates.
Jean-Baptiste Joseph  Fourier  [or  Fourier -Bessel series; or fast  Fourier  transform; or  Fourier transform; or  Fourier  expansion; or  Fourier  series] 