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- Direct FIR filter implementation requires
multiplies and
adds
- TIIR implementation requires 3 multiplies and 2 adds, independent of
- No savings in memory
Note that there is a pole-zero cancellation in the TIIR transfer function
- If
, no problem since the canceled pole is stable
- If
, imperfect pole-zero
cancellation due to numerical rounding
leads to exponentially growing
round-off error
Basic Idea: Since the overall TIIR filter is FIR(N), alternate
between two instances of each unstable one-pole, starting each new one from
the zero state
samples before it is actually used. (Apparently first
suggested by T. Fam at Asilomar-'87 for the case of distinct poles.)
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Download HornModeling.pdf
Download HornModeling_2up.pdf
Download HornModeling_4up.pdf