Trumpet-Bell Impulse Response Computed from Estimated Piecewise-Cylindrical Model

• From pulse reflectometry on trumpet with no mouthpiece
• Bore profile is reconstructed, smoothed, and segmented
• Impulse response of ``bell segment'' = ``ideal filter''
• At $f_s=44.1$ kHz, filter length is $\approx$ 400 to 600 samples
• A length 400 FIR bell filter is too expensive!
• Convert to IIR? Hard because
  • Phase (resonance tunings) must be preserved
  • Magnitude (resonance Q) must be preserved
  • Rise time $\approx$ 150 samples
  • Phase-sensitive IIR design methods perform poorly