Audio Compression

Here is a randomly generated waveform:

Variants of the DCT algorithm are used heavily in lossy audio compression. Because an audio signal is saved as a waveform, expressing it as a sum of cosine waves

obvious here.

np$.$random.seed$(5)$

$x=np.$linspace $(0,2**np.,960)$

$y=np.zero{s}_l$ike$(x)$

for $i$ in range$(15)$:

$y+=np*cos((x+(np*random*rand({)}^{**}10)-5)**(np*random*rand({)}^{**50}))**np*random*rand()$

plt$.$plot $(x,y)$

# This is randomly generated $--$ You can try playing it$,$

# but I can't guarantee you'll like what you hear $$

To simplify things computationally, we will break up the data into smaller chunks of $192$ elements. Why does this help? Lets explore what happens if we try to com

DCT basis of an entire $4$ minute song sampled at $44100Hz$ :

$(4$min$60sec44100Hz{)}^{2}8$ bytes per decimal ~~$900TB$

So$,$ just a bit too much to store in memory. How about for just the smaller chunks?

${192}^{2}8$ bytes per decimal $=288Kb$