Design of Multiplierless Decimation Filters Using an Extended Search of Cyclotomic Polynomials

This brief addresses the design of multiplierless decimation filters using an extended set of cyclotomic polynomials (CPs) as constituent filters. It extends the results presented in a companion paper by one of the coauthors to CPs with indexes in the set
$\{\hbox{1},\, \ldots,\, \hbox{200}\}$
, and it presents the
$z$
-transfer functions of all CPs with indexes from 61 to 200. One of the key observations stemming from the results of this brief is that CPs with indexes in the set
$\{\hbox{105},\, \ldots,\, \hbox{200}\}$
still have very effective coefficients, i.e., integers belonging to
$\{-\hbox{1}, \, \hbox{0}, +\hbox{1}\,\}$
, but
$z$
-transfer functions have to be recursive. Regardless of the application to multirate filters considered in this brief, these polynomials can also be used for designing classical finite-impulse response filters. Moreover, this brief provides guidelines to simplify the design of constituent decimation filters in multistage architectures and to reduce computational complexity of the proposed filters. Finally, comparisons are given with respect to other techniques in the literature.