S$2$ A pressure sensor outputs $2\mathrm{.}5m\frac{V}{k}Pa,$ but there is $60-Hz$ noise of a steady peak $55$ mV on the line. Pressure in the range $0\mathrm{.}0$ to $70$ kPa must be converted by an ADC and presented to a computer. The resolution must be at least $0\mathrm{.}2$ kPa $.$

a$.$ Design a system of filter, signal$-$conditioning, and ADC specifications to satisfy this requirement.

b$.$ Suppose the pressure suddenly changed from $20$ to $50$ kPa $.$ How long would it be before the ADC presented the correct digital signal for this pressure to the computer?