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How to determine the bitwidth of the Halfband filter

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If I design a Multi-stage decimation filter,say:
first stage, CIC filter
second stage, Halfband filter
......

Then , if the bitwidth of CIC filter output is 16bits, what the bitwidth of the Halfband filter would be needed. I have seen some papers, the bitwidth of the Halfband filter are incresed by 0bit, 1bit, 2bits than the first stage respectively. So I have a doubt, is that the bitwidth chosen abrirarily?If not, how to choose it?Thanks for your reply in advance.
 

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