The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-calculus

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: [ap-calculus] Digital analog converter (DAC) making a discrete continuous?
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Paul SooHoo

Posts: 290
Registered: 8/28/09
[ap-calculus] Digital analog converter (DAC) making a discrete continuous?
Posted: Sep 17, 2012 9:45 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

This article caught in the New York Times:

caught my attention because at this time of year I assume you like me are teaching continuity and the classic how can we make (x^2 - 9)/( x - 9) continuous at x = 9? Yeah, I like this problem. You get to review difference of squares, you get to look at its surprising graph, you get to review limits (the left and right are equal), you get to analyze this numerically by looking at the table of values (I definitely am a proponent of the rule of 4) and you get to review the definition of continuity and with a judicious selection of the proper y-value you get to fill in the "hole" and repair the discontinuity. I like all of that but the back of my mind I kept thinking "so what? aka when are we ever going to use this stuff?"

Does anyone know the inner workings of a digital analog converter? Specifically, I know that "normal" sounds are analog and look like sine waves. To make say a CD or an MP3 these analog waves are "sampled" and made into a discrete series of 1 and 0s which I would consider a discontinuous set of data. To reconstitute the music these 1 and 0s need to be reassembled into a analog sound wave.

So am I correct in assuming from the article:

" Later, your sound system will play a sophisticated game of connect-the-dots to turn that choppy data back into a wave. That takes math. How authentic the playback sounds depends largely on how well the system turns digital dots back into the original wave.

That de-digitizing is done by a computer chip and software combination called a digital-to-analog converter (or DAC) ? and here is a little secret of the audio industry ? to keep prices down, manufacturers often scrimp on that part. That means mediocre math."

that the mediocre math the article is referring to is how to accurately fill in the hole as in the classic (x^2 - 9)/( x - 9) example? Any calculus/audiophiles out there that would know whether my supposition is correct? If so I am really excited because it is hard to come up with everyday examples of discontinuous functions other than taxi cabs and making copies and Kinkos :)

PS A fun piece of trivia: most people think a standard CD is solid and opaque. But if you hold a CD up to strong light like sunlight coming through a window you can see through it. Alas, your students are getting to the point where they don't even know what a CD is let alone a 45 (other than a gun) or an LP. Sigh.

Appended to this posting by the moderator:
This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at and post messages there.

Lin McMullin
Calculus EDG Moderator

Course related websites:
To search the list archives for previous posts go to

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.