>> So for every pair of samples, it simply computes the sum and the
>> difference?
>
> Recursively, yes...

Right. Well if you say "it calculates the sum and the difference of each 
pair of samples", suddenly it becomes pretty obvious what it's doing, 
and why it's reversible.

It also explains why the partial reconstructed wave is the shape it is. 
And it suggests that having fewer terms available is going to futz with 
the high frequencies first.

(Then again, this sort of transform is probably more useful for 
time-domain signals like image data rather than frequency-domain data 
like sound.)

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