Re: tfestimate vs fft

[Henry Gomersall]

On Wed, 2013-04-24 at 14:34 +0100, Arnaud Miege wrote:
> On 24 April 2013 14:18, Henry Gomersall <address@hidden> wrote:
>         
>         
>         So what does taking the FFT of that data tell you? You're only
>         going to
>         get something akin to the transfer function if your input
>         signal is full
>         bandwidth.
>         
>         Ideally, you want to whack an impulse into the system and see
>         what
>         happens on the other side. Failing that you can get a pretty
>         good idea
>         of the PSD (and hence the _amplitude_ of the FFT) using white
>         (or
>         whitish) noise as the input, though that doesn't tell you much
>         about the
>         phase.
>         
>         I don't really know what tfestimate is doing, so I can't
>         comment on its
>         reliability, though I'd be far more inclined to trust it than
>         your
>         homebrew estimate, given that presumably it factors in all
>         these issues.
>         
>         Cheers,
>         
>         hen
>         
> 
> 
> Thanks, unfortunately in practice, I can't inject an impulse or white
> noise heater input, as it's part of a closed-loop control system. I
> can however, try to override it, to get a rectangular pulse input into
> the system, which might provide better frequency content.
> 
> 
> tfestimate, from what I can see in the function description, uses the
> Welch method (pwelch) to estimate the cross-power spectral density of
> the input x and output y (Pyx) and the PSD Pxx of x. The transfer
> function is then calculated as Txy = Pyx/Pxx. At least that's what
> MATLAB's implementation of tfestimate does. I assume Octave is the
> same.

The following is probably a good read in this context:
http://dsp.stackexchange.com/questions/2096/why-so-many-methods-of-computing-psd

Do you get a phase measurement from the tfestimate function? I'm a bit
rusty with these techniques, but it seems like a tricky thing to try to
extract.

As a heating device, I presume nothing changes very fast? It might be
enough to give it a blast of heat and then remove it. That could
reasonably modelled as a rectangular pulse with some arbitrary scaling.
I'm beginning to hesitate though as I'm not really a control engineer,
so trying to influence plants and suchlike is not my area.

hen