Can I take the derivative of a function that represents a piece of music? The music is given in .mp3, .midi or whatever comes in handy.
In Mathematica, you can read in .wav files using
Import. Since the data is then a discrete data sequence, you can't take a real calculus-style derivative, but you can take the derivative numerically, for instance, using functions like
DerivativeFilter (thanks Jens). In fact, the derivative operation is a kind of high-pass filter, which will augment the noise and remove the low frequencies. You can listen to the changed sound using
SampledSoundFunction or by saving the result out to a .wav file using
Export. There are plenty of other ways you can manipulate the sound:
HighpassFilter come to mind.