Low-pass digital filtering with the host windowing design technique

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Abstract
This paper gives a detailed description of the host windowing technique of designing low-pass digital filters. The relationship between the quality of the host filter and the resulting low-pass filter is examined both theoretically and in measurement examples. New transfer function symmetry and error bounding results are obtained and experimentally confirmed for variable cut-off filters.It is demonstrated that variable cut-off low-pass filtering can be undertaken in a manner which, in contrast with the normal windowing approaches, gives the designer clearly specified worst case operating conditions across a family of filters for a selected host window. It is shown that the worst case performance of even-length filters built using a Hilbert transform host is better than the worst case obtained for odd-length differentiator hosted low-pass filters. However, for cut-off frequencies around the quarter sampling frequency, odd-length filters often perform significantly better than even ones.Kaiser and minimax hosts are studied and found to perform well; the designer can be sure that, for a given transition width, the peak ripple obtained with these hosts will not exceed about twice the peak ripple that could have been attained through direct (and much more costly) minimax low-pass design. Kaiser designs are slightly better host designs when the filter length is even, but minimax hosts are often better than Kaiser ones for odd-length filters. In all cases the one-off host filter design explicitly establishes the peak ripple and transition width that will arise for any conditions during the use of the host windowing technique.

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