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In this technical note, we present a new frequency weighted balancing related technique which is based on a parametrized combination of the unweighted balanced truncation technique  , and the partial fraction expansion technique  . The reduced-order models which are guaranteed to be stable in the case of double-sided weighting, are obtained by either direct truncation or singular perturbation approximation. Simple, elegant and easily computable a priori error bounds are also derived. Numerical examples and comparison with other well-known techniques show the effectiveness of the proposed technique.