> You can reduce this by using another window function - but then, 
> strictly speaking, you're multiplying your signal by a window, which 
> convolves its spectrum with the spectrum of the window. In other words, 
> by windowing the signal you're blurring its spectrum.

Usually a slightly blurred spectrum is the preferred outcome.  

> So far, everything I've ever learned about DSP seems to hinge on one 
> single equation:
> 
>   sin X + sin Y = 2 cos (X-Y)/2 sin (X+Y)/2
>
> This says many things. But most obviously, it says that the sum of any 
> two waves is also the product of two *other* words, and vice versa. So 
> the question is, at what frequency does a wave become "sound" rather 
> than "variation in sound"?

20 Hz?
 
> The *other* question, of course, is "how many frequency bands do I need?"

Experiment!

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