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Frequency translation of audio signals requires the use of very sharp Hilbert transformer if the low frequency components are to be faithfully translated. Unfortunately, the order of a very sharp Hilbert transformer is very high, resulting in very high arithmetic complexity. The frequency-response masking (FRM) technique has been used very successfully for greatly reducing the complexity of extremely sharp halfband filters. There is a very close relationship between a halfband filter and a Hilbert transformer. In this correspondence, we propose to synthesize a very sharp Hilbert transformer using the FRM technique via the synthesis of a very sharp halfband filter.