Let's assume that system is characterized by the following input/output equation:
y(t)=1000· x(t-200)
where t is given in msec and x(t) in mV.
What time delay in msec would you expect to find the signal relatively to real time?
What range of values in units of Volts would you expect y(t) to have if we assume that the range of x(t) is ±1mV? What are the units of the gain 1000 of the amplifier?
Is the system an LTI system? Explain (Prove)
Find and sketch y(t) when x(t) is a train of action potentials (model the action potentials as δ-impulses) 100 msec apart from each other. Justify your drawing on the basis of your answer in (c) above and related properties of LTI systems and δ(t). [hint: find h(t)]