Re: DFT, energy arrivals, and when to use SMAART vs. Systune
Hi Phil,
My first thought was that, to the extent that the uncorrelated energy varies between frames, yes, averaging will help, but that the same averaging can also be done in an RTA mode where the results of the DFT frames are being shown directly without doing the TF division by the DFT of the reference signal.
However, I realise the TF is not literally calculated as B/A where A is DFT of input and B is DFT of output but that what's actually calculated is (A*/A*)(B/A) or (B*/B*)(B/A), where A* and B* are the conjugates, giving either cross-spectrum/power-spectrum-A, or power-spectrum-B/cross-spectrum*. I understand, in the presence of noise, the two results will be different (and it's the difference between them that's the source for the coherence result). The paper I just checked suggests that the former estimator is better than the latter in the presence of output noise. Unfortunately, I don't have a good enough grasp of this to get a clear view of the improvement rendered relative to averaging a single DFT result. I shall attempt to study further!
I have to say, though, that in the practical examples I've attempted to set up, any immunity to late energy in the averaged TF has been subtle (relative to a similarly-averaged RTA view). My earlier example, for instance, used bucketloads of averages.
Hang on, I didn't say that Smaart was time blind: obviously, there's a phase display (and phase is time), coherence (that will reflect the presence of uncorrelated energy), and impulse response (showing system response entirely in the time domain), none of which exist in an RTA, and I agree with what you say about them. I said that the transfer function magnitude display is time blind if you don't enable an explicit time window (what you're calling a "secondary" window). Subject to your caveat about averaging, I still believe this to be the case.
I wasn't at all seeking to challenge either the cleverness or the usefulness of the dual-channel FT analysis method (or of Smaart), just what seems to be the widespread misunderstanding that the FT time window will inherently serve to exclude energy arriving after the length of the window from the measurement.
Not having used it, I didn't know that this wasn't yet in Smaart 7. Definitely worth implementing.
I've no disagreement with the rest of your post: good insights.
Cheers!
Nick
