1. Draw the system block diagram representation for the continuous and discrete time systems defined below. (a) y(t)- 8x(t)- dy(t)/dt (b) y[n]=x[n] + x[n-1] (c) y[n]=x[n-1]+ y[n-1] The voltage signal Vs(t) from a sensor that was monitoring soil moisture in a farm was applied to the terminals of a passive RC system for irrigation control operations. Suppose output signal voltage Vo(t) monitored across the resistor R, is connected to the irrigation controller system. (a) Sketch the circuit diagram of the passive RC system. (b) Derive a suitable differential equation that describe this system showing the relationship between the input Vs(t) and output Vo(t). (c) Find the discretize time RC system equivalent of the continuous time passive RC system. (d) Using the voltage divider method for the circuit diagram in (a), find the ratio of the output voltage to the input voltage of the system. This will give what we call the transfer function of the system in frequency domain. (e) Using your results in (c), and R=40k, C = SF, and time interval T = 0.4, determine and justify whether this RC system is: (i) linear or nonlinear (ii) time varying or time invariant (iii) memory or memoryless (iv) causal and non-causal (1) Using the differential equation in (b), find the Laplace transform of the equation and find the RC system transfer function (ratio of output to input)