On 8/26/15 9:47 PM, Ethan Duni wrote:
>15.6 dB + (12.04 dB) * log2( Fs/(2B) )
Oh I see, you're actually taking the details of the sinc^2 into account.
really, just the fact that the sinc^2 has nice deep zeros at every
integer multiple of Fs (except 0).
What I had in mind was more of a worst-case analysis where we just
call the sin() component 1 and then look at the 1/n^2 decay (which is
12dB per octave). Which we see in the second term, but of course the
sine's contribution also whacks away a certain portion of energy,
hence the 15.6dB offset.
well, it's more just how the strengths of the images add up.
On the other hand if you're interested in something like the
spurious-free dynamic range, then the simple 12dB/octave estimate is
appropriate. The worst-case components aren't going to get attenuated
at all by the sin(), just the 1/k^2. I tend to favor that in cases
where we can't be confident that the noise floor in question is (at
least approximately) flat.
but whether you're assuming a flat spectrum up to B or just a single
sinusoidal component at the maximum frequency of B, it's the sin() (or
the sin^4 in the power spectrum of the images resulting from linear
interpolation) that is the mathematical force in reducing the image
strength in the oversampled case where 2B << Fs. so it's *both* the
sin^4 *and* the 1/k^4 is used. the 1/k^4 thing is needed for the power
of all those images to add up to a decent finite number. but it's the
sin() that puts a stake in the heart of the image and that is
quantitatively quite useful.
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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