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 compute the DCT basis of an entire $4$

minute song sampled at $44100$

Hz:

$(4$min$\backslash$times $60$sec$\backslash$times $44100$Hz$)2\backslash$times $8$ bytes per decimal$900$TB

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

$1922\backslash$times $8$ bytes per decimal$=288$Kb

That seems better! We will use for this example N $=192.$ We first need to generate the new basis: