For the fourth problem, we will use the MDCT+windowing function from problem #2 on a sample of music. The sample used for this part will be from "♥ (Heart)" by Savant. This audio is of a much higher sample rate (44KHz compared to 8KHz) than previous samples, which is necessary in order to capture the large variety of constantly-changing frequencies being overlapped.

Relevant files: prob1codec.m, prob2codec.m, question4.m, prob4.txt, ♥ (Heart) by Savant.

Original Audio Sample:



Without Windowing:

b = 2, RMSE = 0.0304 Decoded:       Error:

b = 4, RMSE = 0.0081 Decoded:       Error:

With Windowing:

b = 2, RMSE = 0.0276 Decoded:       Error:

b = 4, RMSE = 0.0070 Decoded:       Error:

Compressing with windowing reduces RMSE by a small amount (~10%) but in general both methods perform just as well. Extreme artifacting can be heard at b = 2, but at b = 4 the error becomes less noticeable (helped in part by the high sample rate).