Apparatus, and an associated method, for facilitating frequency offset estimation between communication stations operable in a communication system. A likelihood polynomial is calculated and provided to a filter. The filter forms a filtered representation of the likelihood polynomial, and the filtered representations are down-sampled by a decimator. A sampled, filtered representation of the likelihood polynomial is thereby obtained. The filtered, sampled representation is applied to a root calculator that calculates the roots of the polynomial, thereafter, to be used to compensate for the frequency offset.