It's not exactly Cooley-Tukey. In Cooley-Tukey you take two _interleaved_
DFT's (that is, the DFT of the even-numbered samples and the DFT of the
odd-numbered samples) and combine them into one longer DFT. But here you're
talking about taking two _consecutive_ DFT's. I don't think there's any
cheap way to combine these to exactly recover an individual bin of the
longer DFT.

Of course it's possible you'll be able to come up with a clever frequency
estimator using this information. I'm just saying it won't be exact in the
way Cooley-Tukey is.


On Mon, Nov 5, 2018 at 12:28 AM, gm <> wrote:

> Am 05.11.2018 um 01:56 schrieb gm:
>> so you do the "radix 2 algorithm" if you will on a subband, and now what?
>> the bandlimits are what? the neighbouring upper and lower bands?
>> how do I get a frequency estimate "in between" out of these two real
>> values that describe the upper and lower limit of the band but have no
>> further information?
>> thank you.
> The way I see it:
> If you do that 2 point transform on a band you get 2 data points instead
> of one (or rather instead of two sucsessive ones of course), representing
> the upper and lower bandwith limit of the band, but not very well seperated.
> But if you take the result of the previous frame also into account you now
> get 4 points representing the corner of a bin
> of the original spectrum so to say, however in bewteen spectra, and you
> now can do bilinear interpolation between these 4 points.
> But in the end this is just crude averaging between two sucessive spectra,
> and I am not sure if it sounded better
> or worse. It's hard to tell a difference, it works quite well on a sine
> sweep though.
> But there must be a better way to make use of these 2 extra data points.
> In the end you now have the same amount of information as with a spectrum
> of double size.
> So you should be able to obtain the same quality from that.
> That was my way of thinking, however flawed that is, I'd like to know.
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