INTERRELATIONS BETWEEN THE COEFFICIENTS OF FIR DIGITAL DIFFERENTIATORS AND OTHER FIR FILTERS AND A VERSATILE MULTIFUNCTION CONFIGURATION

Interrelationships between seven types of digital FIR filters, viz. th e differentiators (DD), Hilbert transformers, half-band lowpass/highpa ss filters, bandpass/bandstop filters and frequency discriminators, ha ve been established. It has been shown that all the aforementioned fil ters can be derived from the design of a DD. If we use the optimality criteria of maximal linearity of the frequency response of a different iator, the proposed relations yield maximally flat/linear frequency re sponses for the remaining six filters. Similarly, an equiripple relati ve error design of a DD gives equiripple filters through the use of th e suggested interrelations. A versatile, multipurpose, FIR configurati on has also been proposed which yields optimal frequency response for all the seven types of digital filters. The suggested design is shown to be particularly useful for operation over the frequency ranges 0 le ss-than-or-equal-to omega less-than-or-equal-to 0.50pi (0.50pi less-th an-or-equal-to omega less-than-or-equal-to pi) for lowpass (highpass) filters and 0.25pi less-than-or-equal-to omega less-than-or-equal-to 0 .75pi for the remaining ones. Mathematical formulas for computing the weights of aforementioned filters have also been derived. Possible use s of the suggested design have been given.