>On 29 Jun, 07:37, "Michael Plante" <michael.pla...@gmail.com> wrote:
I have a very long data series sampled at 100 Hz,
>
>What does 'very long' mean?

Probably as much as half an hour. The operators tend to get tired afte
some time, and batteries die in a couple hours. However, I have abou
11 hours of data without the sinusoid of interest that I used to find a
Allan variance.


>> and I know
>> that the signal of interest is roughly sinusoidal and in the range o
0.2=
>5
>> to 0.5 Hz (it is a physical oscillation of a plant). =A0The frequenc
may
>> shift slightly within that band over time, and the amplitud
definitely
>> changes.
>
>What's the typical time scale of these fluctuations?

It's hard to say. That's one thing I'm going to look at. In reality, I'
doing this on each of six channels of
manufacturer-temperature-compensated (so they claim) MEMS IMU. Th
readings are from an underwater vehicle, and it is vertically stable, so i
oscillates when disturbed. From just looking at the signal, though, it'
hard to figure out...even when I've done my crude smoothing. It may b
possible to get you the time scale, but, in light of my clarifications
would it be helpful?


>>=A0I know there is a small random walk and some white noise, and
>> possibly some well-separated-in-frequency sinusoidal noise components.
>
>Overharmonics of the fundamental or unrelated with
>the fundamental? What about aliasing? Are there
>anti-alias filters prior to the sampling step?

I suspect the other components are unrelated. Possibly noise from fan
and such. There is an antialias filter at 40 Hz on each rate gyro, and 5
Hz on each accelerometer, and both are, I believe, analog 5-th orde
elliptic filters, but it's a very tiny OTS board, so I only have vague doc
from the manufacturer, as well as documentation on the chips they're using


>> MAIN POINT: =A0I need a good (ideally, best) estimate of the actua
value=
> of
>> the sinuosoid at each sample point, along with an estimate of the
>> derivative.
>
>What 'value' is this? Frequency? Amplitude? Both?

Neither...a cleaned-up time domain signal. Instantaneous amplitude, i
you will. Plus the derivative...


>Depending on the details, there are several possible
>approaches:
>
>- Adaptive filters.
>- Phase-locked loops.
>- Kalman filters.
>- Frequency estimators.
>
>You might get more useful answers if you describe both
>the process and the goal for the analysis in more detail.

Sorry...I wanted to keep the first post short. Again, the actua
frequency doesn't interest me so much as the fact that I suspect I can us
it to do a better job of filtering undesired components. I don't want t
use a Kalman filter because I prefer to keep my smoothing unbiased b
potentially-faulty system models at this point (more likely, I just don'
have appropriate coefficients yet). A phase-locked loop sounds attractive
now that you mention it, though I'll have to go study them some more. M
last attempt at one (for a different app) converged very slowly.





****
Tim Wescott wrote:
>> plain old bandpass filter

My problem with that (and maybe it's just my lack of experience wit
digital filters) is that I thought that would introduce a phase delay.
Again, I am more interested in the value at a given time. To a certai
extent, if it's exactly the same (phase-?) delay over the whole passband
I'd be okay, but I was hoping for some sort of sinusoidal interpolatio
scheme. A relative phase between the channels has physical meaning (e.g.
pseudoforces would be an input to help me figure out where the center o
mass is, I think). I have written dynamic equations, but I wish to clea
up the channels individually first. I would not expect a phase change ove
the passband to matter if it were a purely sinusoidal signal, but it'
probably not a "sharp" frequency peak, regardless of how you process it.