Real halfband lowpass and complex halfband bandpass filters, versatile building blocks in a multitude of DSP applications, are revisited with focus on efficient implementation. Linear-phase FIR and minimum-phase IIR halfband filters are recalled predominatly for sample rate alteration, their computational loads are compared, and optimum signal flow graphs are presented. The same comparisons are carried out for the corresponding complex halfband filters (Hilbert-transformers with their passbands centred at the normalised frequencies of Omega(c) = +/-pi/2) with and without an additional frequency offset by Delta Omega = +/-pi/4. As expected, the smaller the transition width between passband and stopband, the higher the relative advantage of the IIR approach in terms of computation. Yet, there exist ranges of specifications where linear-phase FIR halfband filters outperform their minimum-phase IIR counterparts - even without taking into account the linear-phase and stability advantages of FIR filters.