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Abstract
Digital differentiators (DD) are extensively used in various computational systems. An ideal DD has the frequency response given by Hd(w)=jw,—n≤w≤π. The most popular FIR design for the differentiators is the minimax relative error (MRE) approximation, proposed by Rabiner and Schafer [1], The MRE-DDs are, in general, suitable for wideband frequency ranges with moderate accuracy, (say, 100±1%) but are not flexible enough to be efficiently adopted for limited (low, mid or high) frequency bands. Moreover, the required weighting coefficients for these DDs are computed by using an optimization algorithm [2]
In this review paper, we discuss a new class of digital differentiators, recently investigated by us, which have maximally linear (ML) frequency response at w=0 or w=π/2 or w=π. Correspondingly, this design yields efficient approximations for low, mid or high frequency ranges, giving extremely low relative errors (RE). A universal digital differentiator has also been obtained, which covers the frequency range 0≤w≤0.90π. Mathematical formulas for computing the exact values of the weighting coefficients have also been given.
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