This problem requires developing a signal and systems model corresponding to one of the behavioral intervention...

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This problem requires developing a “signal and systems" model corresponding to one of the behavioral intervention responses in Figure 17 of the Glass et al. text (the figure is included in the lecture presentation on first-order systems). Please examine the response from an intervention participant (y(t)) as shown in Figure 1. The intervention is represented by the input signal u(t) in Figure 1, which is a unit step change (0 before the intervention is applied, 1 afterwards). For this intervention participant, please do the following: a) Obtain the Laplace transform model corresponding to the signal y(s) and to the transfer function p(s) between y(s) and u(s). Hint: recognize the basic signals and operations that are reflected in y(t), and the Principle of Superposition. b) Express the transfer function p(s) as a differential equation in time. Delayed Change in Level t=0 t=a t=b Time t=0 Time Figure 1: Time-domain response (y(t)) to treatment (u(t)) in a behavioral intervention. Input Signal u(t) Output Signal y(t) This problem requires developing a “signal and systems" model corresponding to one of the behavioral intervention responses in Figure 17 of the Glass et al. text (the figure is included in the lecture presentation on first-order systems). Please examine the response from an intervention participant (y(t)) as shown in Figure 1. The intervention is represented by the input signal u(t) in Figure 1, which is a unit step change (0 before the intervention is applied, 1 afterwards). For this intervention participant, please do the following: a) Obtain the Laplace transform model corresponding to the signal y(s) and to the transfer function p(s) between y(s) and u(s). Hint: recognize the basic signals and operations that are reflected in y(t), and the Principle of Superposition. b) Express the transfer function p(s) as a differential equation in time. Delayed Change in Level t=0 t=a t=b Time t=0 Time Figure 1: Time-domain response (y(t)) to treatment (u(t)) in a behavioral intervention. Input Signal u(t) Output Signal y(t)