Task: Text Categorization
Input (English): In 1981, Takeda et. al devised a method for fringe-pattern analysis that used this operation to detect small phase variations. Performing this operation on a Dirac comb returns itself. Applying this operation to a function that is in L1 and L2 will necessarily result in a product in L2 by Plancherel's theorem. This operation is unitary by Parseval's relation. Performing this operation on any constant function yields the Dirac delta function, while performing this operation on an image can decompose it into a sum of sines and cosines. Cooley and Tukey developed an algorithm for implementing its "fast" variety. For 10 points, name this transformation that takes an input in the time domain and maps it to the frequency domain.
Output (English): Science