Application of the generalized short time DFT to the Hilbert transformer and its characteristics

A new class of signal processing is introduced by generalized short time discrete Fourier transform (DFT) in which sub-channels are arbitrarily adjusted on the objective frequency domain. An implementation of the noble Hilbert transformer that employs this ST gDFT is discussed. Restricting the ST gDFT within causality, the phase shifting error of the implemented Hilbert transformer is less than a micro degree. Its amplitude error is shown to be less than 0.01 dB.