Matlab : Exploring the effects of co-efficient quantization

Question

b = [0.9355,-3.6135,5.3603,-3.6135,0.9355]
a = [1,-3.7339,5.3562,-3.4929,0.8752]

Use MATLAB to quantize the coefficients in the vectors a and b to 16 bits of precision. First, take each vector and divide by the smallest power of two such that, after division, the magnitude of the largest filter coefficient is no larger than 1. Next, multiply the resulting vectors by 2¹⁵, and round to the nearest integer. (You can use the round function.) Divide the resulting vectors by 2¹⁵. The resulting values should be no less than -1 and no larger than 1. Finally, multiply these values by the power of two by which you originally divided.

I do not understand what that smallest power of two is! Can someone help me out with the code? Thanks!

Answer 1

For each of the vectors "a" and "b", you need to find the element with the largest absolute magnitude. (I'm not sure of the specific Matlab code for this; probably something like max (abs (a)).)

Then, you need to pick the smallest number of the form 2^N (N is an integer) that is larger than the value determined in the previous step.

From there, the rest of the instructions should be straightforward.