Design of FIR LS Hilbert Transformers Through Fullband Differentiators

This paper presents some new explicit expressions for the impulse responses of the case 3, case 4, and differentiating Hilbert transformers. The proposed closed-form design is based on the fullband least-squares differentiator and relations between differentiator and Hilbert transformer. The obtained simple formulas give an efficient way to determine tap-coefficients of designed Hilbert transformers even with a hand calculator. Several numerical examples and comparison with McClellan-Parks algorithm prove the efficiency of this approach.