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filter, given as {\tt numerator}. The filter coefficients can be
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designed using one of the designed functions,
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e.g. \Ref{design_FIR_filter}. Double filtering is performed by
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again and reversing the waveform again. Normal filtering will impose a
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lag on the signal depending on the order of the filter. By filtering
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the signal forwards and backwards, the lags cancel each other out and