This is part formula of command-response model (Fujisaki Model):

Analysis and synthesis of fundamental frequency contours of Standard Chinese using the command–response model 

http://www.sciencedirect.com/science/article/pii/S0167639305001706 Why they are critically-damped second-order linear systems?

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  • $\begingroup$ i have no idea what $G_\mathrm{t}(t)$ is. it is not the impulse response of an LTI system with that $\min[.]$ function in there. the reason the $G_\mathrm{p}(t)$ is critically damped is that the expression with form $h(t) \ = \ t \ e^{-\alpha t}$ is the inverse Laplace Transform of something like $$ H(s) \ = \ \frac{1}{(s+\alpha)^2} $$ anything less damped than that will have a sinusoid in the impulse response (it "rings"). anything more damped than that has two decaying exponential functions (with different $\alpha$). $\endgroup$ – robert bristow-johnson Nov 4 '14 at 3:19
  • $\begingroup$ What do you mean by "s" in the denominator of your formula? $\endgroup$ – Ping Tang Nov 4 '14 at 3:28
  • $\begingroup$ Laplace transform $\endgroup$ – robert bristow-johnson Nov 4 '14 at 4:40

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