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Closed-Form Design of Maximally Flat IIR Hilbert Transformer With Integer Delay

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3 Author(s)
Soo-Chang Pei ; Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan ; Huei-Shan Lin ; Peng-Hua Wang

This paper presents the closed-form designs of an infinite-impulse-response (IIR) Hilbert transformer with an integer delay. The maximally flat criterion is applied at the midband frequency π/2. These designs are further categorized into eight types according to the filter orders and the delay values being even or odd. Their coefficients can be explicitly solved in closed form. A recursive relation also exists, facilitating the computation of these coefficients. Moreover, under the suggested relations and formula for the design parameters based on the Eneström-Kakeya theorem, we can obtain a satisfactory stable IIR Hilbert transformer.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:57 ,  Issue: 11 )