On 29 Jun, 07:37, "Michael Plante" <michael.pla...@gmail.com> wrote:
> Hi all,
>
> I'm trying to postprocess a signal that contains a low-frequency sinusoid,
> but my DSP skills are mediocre (I've had formal classes in continuous time
> systems). *I have a very long data series sampled at 100 Hz,

What does 'very long' mean?

> and I know
> that the signal of interest is roughly sinusoidal and in the range of 0.25
> to 0.5 Hz (it is a physical oscillation of a plant). *The frequency may
> shift slightly within that band over time, and the amplitude definitely
> changes.

What's the typical time scale of these fluctuations?

>*I 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?

> MAIN POINT: *I need a good (ideally, best) estimate of the actual valueof
> the sinuosoid at each sample point, along with an estimate of the
> derivative.

What 'value' is this? Frequency? Amplitude? Both?

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.

Rune