Abstract

A new approach for the design of recursive fullband digital differentiators using parallel all-pass structure is discussed in this paper. While magnitude response of designed fullband differentiator approximates the ideal one in the weighted Chebyshev sense, its phase response is a nearly-linear function of frequency at low frequencies. The low-pass differentiators, presented in this paper, are obtained by cascading the proposed recursive fullband differentiators with the corresponding low-pass filters. The phase response linearity error of such low-pass differentiators is shown to be primarily affected by the phase response nonlinearity of the utilized low-pass filter. A comparison with some of the existing fullband and low-pass differentiators shows that proposed differentiators require less multiplications, while their phase and magnitude responses are either better or slightly worse than those of existing differentiators.

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