This operation is related to the autocorrelation function by the Wiener- Khinchin theorem, and its "fractional" extension is used as a noise filter and allows this operation to be applied a non-integer number of times. When p is between one and two inclusive, this operation goes from Lp to Lq [ell-pee to ell-queue] where q is the reciprocal of one minus one over p by the Hausdorff- Young inequality. This operation is extended to locally compact Abelian groups by the Pontryagin duality, and it is unitary by Parseval's theorem. The recursive Cooley-Tukey algorithm may be used to calculate a "dis
This operation is related to the autocorrelation function by the Wiener- Khinchin theorem, and its "fractional" extension is used as a noise filter and allows this operation to be applied a non-integer number of times. When p is between one and two inclusive, this operation goes from Lp to Lq [ell-pee to ell-queue] where q is the reciprocal of one minus one over p by the Hausdorff- Young inequality. This operation is extended to locally compact Abelian groups by the Pontryagin duality, and it is unitary by Parseval's theorem. The recursive Cooley-Tukey algorithm may be used to calculate a "discrete" one. This operation is applied to produce readable NMR spectra, and is defined such that g of zeta is equal to the integral over all x of the function of x times the exponential of negative two pi i x zeta. FTP, name this operation that moves from a time domain to a frequency domain.
This operation is related to the autocorrelation function by the Wiener- Khinchin theorem, and its "fractional" extension is used as a noise filter and allows this operation to be applied a non-integer number of times.
{Fourier transform}