Summation of continuous band of frequencies

[cmorriss]

Just got a "thought experiment" question from a colleague. The question, as phrased was: If an audio signal was composed by adding all of the frequencies in the audible range, what would it sound like?

I thought it was interesting, so I attempted to solve it by integral. My calculus skills have always been suspect, however, so I would appreciate some feedback.

If each component can be described as sin(f*x), where x is time and f specifies the frequency, then each moment of the resultant signal is the integral of sin(f*x) from f_low to f_high, treating x as a constant.

This should simplify to F(x) = cos(f_low*x)/x - cos(f_high*x)/x which describes the entire signal.

Anything wrong with that?

 

[trambolin]

It's frequency spectrum would be a rectangular function. Hence in time domain it is the sinc function. If I got the question correctly

 

[chroot]

You don't need to use any math. If the signal contains equal energy in all of the audible frequencies, then it is called "white noise." You're probably already familiar with white noise, as it is produced (approximately) by everything from waves crashing against rocks, to fans running at high speed.

- Warren