Complexity and Storage-Cost

$$H_{\rm FIR}(z) = \frac{B(z)-z^{-N}B'(z)}{A(z)}$$

$N$ = FIR order and let $P$ = $A(z)$ order (#poles)

• The computational cost of the general truncated $P$ -th order IIR system is $3P+1$ multiplies and $3P-2$ adds, independent of $N$
• Net computational savings is achieved when $N>3P$

Storage Requirements

• $P$ output samples for the IIR feedback dynamics $A(z)$
• $N$ input samples of the FIR filter (main delay line)
• $P$ input samples for $B(z)$ (normally in delay line)
• $P$ input samples for $B^\prime(z)$ (also possibly in delay line)

Thus, we need a total of at least $N+P$ input delay samples, of which only $2P$ are accessed, and $P$ output delay samples. This is between $P$ and $2P$ more than a direct FIR implementation.