Task: Text Categorization
Input (English): Its Mukai variety is useful in defining abelian varieties, and the essentially identical Plancherel theorem and Parsevals theorem show that it is unitary and applying one of these to a Dirac comb will result in another Dirac comb. It is integral to the Nyquist-Shannon sampling theorem, and both Bluestein's algorithm and Rader's algorithm compute a form of it by transforming it into a convolution, while runtime big-O of n log n for one variety of them is achieved by recursively breaking it down into smaller ones, a technique known as the Cooley-Tukey algorithm. Commonly used in signal and image processing, FTP, name this mathematical operation that breaks a function down into a spectrum of its component sinusoidal frequencies.
Output (English): Science