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Q1. (a) How many levels of quantization does a 12-bit analogue-to-digital converter have? Why is there a quantization error, and how is the error reduced? [3 marks] (b) What is the analogue low-pass filter applied before an analpgue-to-digital converter used for? [3 marks] (C) The temperature of a heater y(t) in degrees celsius satisfies the following differential equation dy (t) + 2y(t) = 48x(t) dx where x(t) is the electric input in volts. Convert the continuous system represented by the above differential equation to the corresponding digital system represented by a difference equation for the electric input x[n], output temperature y[n], and the sampling interval T. [4 marks] (d) Let n be the sample number and u[n] be the unit step function (-0<n<). A rectangle window function is given by u[n]=u[n]-u[n–8] and a cosine function is given (2n-7) by x[n] = 0.54+0.46cos- Applying the window function, calculate the windowed 8 cosine function x[n]. w[n]. (4 marks] (C) A system described by: y[n]=0.5y[n-1]+x[n]+0.4x[n- 1] A unit impulse S[n] and a unit step u[n] are applied as the input, respectively. For each input evaluate the system output y[n] in the time domain up to n=4. [6 marks]