Consider the hypothesis that an isolated hair cell (the sensory cell within the cochlea) can be modeled as a linear system when a pure acoustic tone is the input and the rate of neural firing is the output. Answer the following questions about the system.
(a) Do you believe that this is a linear system? Describe your rational using your knowledge of physics, physiology, and linear systems.
(b) Do you believe that this is a shift invariant system? Describe your rational using your knowledge of physics, physiology, and linear systems.
(c) Design an experiment of set of experiments which could be used to test your hypothesis from part a. Be sure to explain which results would prove or disprove your hypothesis.