The following questions are about how to determine the function f: (l, h) → { 2b – 1}, for an accelerometer, which given a proper acceleration x yields a digital number f(x). we will assume that x has units of "g's," where lg is the acceleration of gravity, approximately g = 9.8meters/seconda. (a) let the bias b e {0, 2b – 1} be the output of the adc when the ac- celerometer measures no proper acceleration. how can you measure b? (b) let a e { 2b - 1} be the difference in output of the adc when the ac- celerometer measures og and lg of acceleration. this is the adc conversion of the sensitivity of the accelerometer. how can you measure a? (c) suppose you have measurements of a and b from parts (3b) and (3a). give an affine function model for the accelerometer, assuming the proper acceleration is x in units of g's. discuss how accurate this model is. (d) given a measurement f(x) (under the affine model), find x, the proper accel- eration in g's. (e) the process of determining a and b by measurement is called calibration of the sensor. discuss why it might be useful to individually calibrate each particular accelerometer, rather than assume fixed calibration parameters a and b for a collection of accelerometers.
(f) suppose you have an ideal 8-bit digital accelerometer that produces the value f(x) = 128 when the proper acceleration is og, value f(x) = 1 when the proper acceleration is 3g to the right, and value f(x) = 255 when the proper acceleration is 3g to the left. find the sensitivity a and bias b. what is the dynamic range (in decibels) of this accelerometer? assume the accelerometer never yields f(x) = 0.