Least-squares design technique for digital Hilbert-transform filters

Discrete-time calculation of Hilbert transforms is of increasing importance in digital processing of communication signals. The technique for designing digital Hilbert filters described here makes use of the properties specific to this filter category in arriving at a simple closed-form matrix formulation. The optimality criterion utilised is that of least-squares error (l.s.e.), which results in filter error characteristics that compare reasonably well with minimax designs using the Remez exchange algorithm¿achieved with considerably reduced computational burden.