On the Behavior of Minimax FIR Digital Hilbert Transformers

Hilbert transformers have been used in a variety of applications including radar systems, speech processing systems, modulation systems, and schemes for efficient sampling of a real bandpass signal. 1,2 Although the theory of discrete Hilbert transformer systems is well understood, it is only recently t h a t design techniques have become available for obtaining optimum (in a minimax or Chebyshev sense) finite-duration impulse response (FIR) approximations to the ideal Hilbert transformer. 3 - 4 It is the purpose of this paper to present new design data on minimax F I R Hilbert transformers to aid in selecting the most efficient network to meet given design specifications. Herrmann 3 has already given a small table of data on F I R Hilbert transformers ; however, the generality and widespread applicability of the data presented here justify this more complete elaboration of the properties of the minimax Hilbert transformer approximations.