A variational approach to the extraction of in-phase and quadrature components

A variational approach is used to define the carrier frequency and the in-phase and quadrature components of a real-valued pulse-like signal. This approach produces a representation in which the in-phase and quadrature components have the smallest possible amount of functional variation. The variational theory is compared with the standard theory of Gabor. The two theories are found to produce essentially the same results for narrowband signals, but in the wideband case, they can differ by an extent that might be significant for the processing of Doppler perturbed radar data.