I would like for you to do some reading from 
    http://eamusic.dartmouth.edu/~book/index.html
as we move through the course. For ECE and EE students some of this is old 
familiar material. This e-book is a course developed at Dartmouth in math 
analysis (Fourier, ...) and music (sound signals). 
Fourier series, and the FFt are in Chapter 3, which begins at 
  http://eamusic.dartmouth.edu/~book/MATCpages/chap.3/3.3.Fourier_sum_sines.html
Sometimes it may help to return to an earlier chapter for some 
background, but you will find the reading easy going. Wavelets are only briefly 
mentioned at the end of this chapter. This book gives you a good sense
historically why wavelets might be important. 
The first chapter (you can begin 1/2 down the page ...)
   http://eamusic.dartmouth.edu/~book/MATCpages/chap.1/1.1.what_is.html
describes sound as a signal produced by changes in pressure. You will need
to press the button to load applets and restart your browser, if the applets
do not load automatically.  The applets in Section 2 of Chapter 1 
will let you easily experiment with modifying the digital sound waves 
via their discrete representation.
   http://eamusic.dartmouth.edu/~book/MATCpages/chap.1/1.2.amp.html
There is a lot here, so search around to see connections to our course. 

For sure run the applet 
  http://eamusic.dartmouth.edu/~book/MATCpages/applethtml/ch1_hear_ticks_to_tone.html
so that you can experiment to see how discrete digital ticks become interpreted 
by your senses as tones.

Shannon sampling will be coming up shortly.