infinite impulse response - What's the advantage of adaptive IIR filter against FIR?

Adaptive IIR filters is not straightforward, and may be unstable. Many people say that adaptive IIR filters use less coefficients than FIR filters. What I'm curious about is how many coefficients can IIR save?

I tried to use adaptive IIR filters to estimate transfer function of a 32-order FIR filter. Assume the IIR filter has $M+N+1$ coefficients: $a_1, a_2, ..., a_M, b_0, b_1, ...b_N$. I found the estimation result is acceptable only when $M+N+1 \ge 30$, i.e. only 2 coefficients can be saved.

In actual projects, for example, a 50 MHz FPGA, a 32-order FIR will produce about $(32 / 50 ~{M}) / 2 = 0.32 ~{\mu s}$ delay, so

• What will happen for IIR?


• Can adaptive IIR filters really reduce number of coefficients and reduce signal processing time delay?