On the optimization of the prototype filter used in the short time DFT Hilbert transformers

Superior characteristics of the short-time DFT (discrete Fourier transform) Hilbert transformer are obtained through an ideal prototype filter of infinite frame number. From the practical application viewpoint, it is important to reduce the frame number of this prototype filter and the processing amount in DFT Hilbert transformers. Optimization of the prototype filters is discussed for realizing small frame number filters equal to the infinite frame number filter in the functional facilities for nonlinear programming and functional analysis. The prototype filters are optimized in the sense of minimizing the ripples both on the passbands and elimination-bands and of achieving sharpness of the mainlobe