Suppose a random variable has a PDF given by

Following the procedure laid out in given example, write a MATLAB program to design an optimum 4-bit (16 level) quantizer for this random variable. Compute the SQNR in decibels of the quantizer you designed. How does this SQNR compare with that obtained in Example. Can you explain any differences?

Example:

In this example, we generalize the results of the last example for an arbitrary number of quantization levels. When the number of quantization levels get large, the number of equations to solve becomes too difficult to do by hand, so we use MATLAB to help us with this task.