For the third problem, we will use the MDCT+windowing function from the previous problem to compress chords of multiple tones layered on top of one another. For the sake of demonstration, a basic C Major chord (C-E-G-C) will be compressed at different degrees of bit quanitzation.

Relevant files: prob2codec.m, question3.m, and prob3.txt.

\( b = 2 \)	\( b = 3 \)
\( b = 4 \)	\( b = 5 \)
\( b = 6 \)	\( b = 8 \)

As expected, higher values of \(b\) produce more accurate approximations. At \(b = 8\), next to no error can be heard. Plotting # of quantization bits vs RMSE shows a roughly logarithmic relationship, with each extra bit of precision cutting error roughly in half:

\(b\)	2	3	4	5	6	8
rmse	0.01449	0.00727	0.00378	0.00211	0.00115	0.00036