A unified treatment of approximation and realization of type-3 finite impul
se response (FIR) linear-phase Hilbert transformers is presented, A simple
method based on Bernstein polynomials and half-band filters is proposed to
derive the transfer function of the system, and a triangular array realizat
ion based on the de Casteljau algorithm is developed from the Bernstein for
m of the transfer function. It is shown that the array structure, consistin
g of multiplierless identical modules, can be realized hierarchically using
complex and real signal processing techniques.