  Linear systems such as room acoustics and string oscillations may be modeled
as the sum of mode responses, each characterized by a frequency, damping and
amplitude. Here, we consider finding the mode parameters from impulse response
measurements, and estimate the mode frequencies and decay rates as the
generalized eigenvalues of Hankel matrices of system response samples, similar
to ESPRIT. For greater resolution at low frequencies, such as desired in room
acoustics and musical instrument modeling, the estimation is done on a warped
frequency axis. The approach has the benefit of selecting the number of modes
to achieve a desired fidelity to the measured impulse response. An optimization
to further refine the frequency and damping parameters is presented. The method
is used to model coupled piano strings and room impulse responses, with its
performance comparing favorably to FZ-ARMA.
