Exercise 4: Sensor Calibration The following questions are about how to determine the functionf: (L, H) → {0, ., 2B – 1}for an accelerometer, which given a proper acceleration r yields a digital number f(r). We will assume thatr has units of "g's", where g is the acceleration of gravity, approximately g = 9.81 m/s².1. Let the bias be {0,..,2B – 1} be the output of the ADC (analog-to-digital converter) when theaccelerometer measures no proper acceleration. In practice, how can you measure b?2. Let a e {0,...,2B – 1} be the difference in output of the ADC when the accelerometer measures 0gand lg of acceleration. This is the ADC conversion of the sensitivity of the accelerometer. In practice,how can you measure a?

Given: The objective is to determine the function f : (L, H) →{0, . . . , 2B -1} for an accelerometer, which gives a proper acceleration x yields a digital number f(x). Assume that x has units of "g's", where g is the acceleration of gravity. approximately g=9.81 m/s2. To find: 1. Let the bias b∈{0, . . . , 2B -1} be the output of the ADC (analog-to-digital converter) when the accelerometer measures no proper acceleration. In practice, how can you measure b? 2. Let a∈{0, . . . , 2B -1} be the difference in the output of the ADC when the accelerometer measures 0g and 1g of acceleration. This is the ADC conversion of the sensitivity of the accelerometer. In practice, how can you measure a? (a) The bias b∈{0, . . . , 2B -1}, the accelerometer measures no proper acceleration: Answer: If the accelerometer is placed horizontally such that there is no component of gravity along the axis being measured. Then according to the theory, the accelerometer can also be placed in freefall in the Vaccum. It would require a more complicated experimental setup rather and it is also required that the accelerometer should not twist when it falls. (b) a∈{0, . . . , 2B -1}, the accelerometer measures 0g and 1g of acceleration, the ADC conversion of the sensitivity of the accelerometer: Answer: When the accelerometer is placed at rest such that the gravity is along the axis being measured, then subtract b.