On the Behavior of Minimax Relative Error FIR Digital Differentiators

摘要: Optimum (in a minimax relative error sense) linear phase FIR digital differentiators can be designed in an efficient manner using Remez optimization procedure. This paper presents data on wideband with even and odd values of N, the filter impulse response duration samples. Based these data, several interesting observations made, including: (i) Differentiators N have peak errors which are approximately one to two orders magnitude smaller than identical bandwidth same number multiplications per sample direct convolution realization. (ii) The differentiator, faster decrease increasing N. (iii) larger value decreasing bandwidth. These lead conclusions that differentiator should made as small possible, used whenever possible. Complete tables coefficients included for