On the Behavior of Minimax Relative Error FIR Digital Differentiators

bandwidth that even of values wideband of a values of the differ- In the past few years a great deal of work has been done in devising filter design techniques capable of obtaining optimum approximations (in the Chebyshev or minimax sense) to a prescribed frequency response characteristic. A general-purpose algorithm now exists 1 for the design of such optimum linear phase finite-duration impulse response ( F I R ) approximations to any desired multiband filter, differentiator, or Hilbert transformer. Since differentiators are an integral 333 part of many practical systems, 2-4 it is the purpose of this paper to present new data on the characteristics of optimum F I R differentiators, as an aid in making informed decisions concerning their use.