We are given an RLC series circuit (below) driven by a noisy voltage source Vin (t), and we use a measurement instrument that linearly amplifies by K and measures the corresponding output voltage. We...

We are given an RLC series circuit (below) driven by a noisy voltage source Vin (t), and we use a measurement instrument that linearly amplifies by K and measures the corresponding output voltage. We know that the input voltage is contaminated by and additive noise source, w(t) with covariance, Rww and the measured output voltage is similarly contaminated with noise source, v(t) with Rvv .

(a) Determine the model for the measured output voltage, Vout(t) (measurement model).

(b) Determine a model for the circuit (process model).

(c) Identify the general model-based processor structures depicted. In each scheme specify the models for the process, measurement and noise.