(a)
Given sensor signal 
We need to eliminate the sensor offset voltage 1.8 and amplify the remaining sinusoidal voltage to 
range.
Given circuit diagram is differential amplifier.
Output voltage expression
From the above expression we can say that the following two points to get the required constraints.
1. For elimination offset voltage(1.8) we have take
................ (1)
2. For achieving a gain range of 
we need to consider that
..................... (2)
From equation (2) we can get
Consider 
, then
Now equation (1) becomes
So to achieve all conditions mention in part (a), we have to take the parameters as like below:
; 
;
(b)
We have to design a filter such that it will attenuate all the frequncies above 1kHz and allow all frequencies below 1kHz.
So we have to design a low pass filter with a cutoff frequency 
.
In case of simple RC passive low pass filter cutoff frequency 
Assume 
,
The filter circuit is as below:
I hope this helps you...............