Order 8 Hankel-Norm IIR Fit to Length 561 FIR (Evidence of Numerical Failure in Previous Example)

• Halving the order actually looks better (``can't happen'')
• Error plot indicates numerical troubles here as well
• An order $P$ IIR filter is made using $P$ th eigenvector of the $561\times 561$ Hankel matrix (condition number = 51751075)
• Numerical failure occurs at the higher orders we need
• Slow rise time of impulse response causes ``numerical stress'' on all phase-sensitive IIR design methods when the IIR order is much less than the rise time