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1. ### A Minimum sample length to estimate the frequency of a sinusoid

"When you sample a signal, don't you have to sample at a freq twice the original? That would be a half wavelength which is what you originally thought." -> If I understand it correctly, that's "Nyquist frequency", yes.
2. ### A Minimum sample length to estimate the frequency of a sinusoid

"Then I would think it would be a pretty small number. Is there a reason that you have groups of 3 points in a row circled in the above plot?" -> just to illustrate that 1) it can be at any random point and 2) 3 is enough for my method. "The problem is that commercial applications involve...

Yes
4. ### A Minimum sample length to estimate the frequency of a sinusoid

Given a discretely sampled horizontal sinusoid of length p, and unknown amplitude, what is the minimal number of consecutive points on a window that is required to correctly estimate its total length, starting at any random point on the wave? Initially I would think it would be either p (full...

6. ### A Fitness function for window length of filter

Fitness function for window length of filter On a sinusoidal signal with amplitude 1, and period P, an exponential moving average (EMA) (with alpha = 1/n), and a linear weighted moving average (LWMA) (with window length n) are calculated; when you subtract the EMA from the LWMA, it can be seen...
7. ### A Difference of WMA & EMA on a sinusoid becomes superposed?

I wrote the code for the image posted above myself in r. So yes, I did write down the formulas.
8. ### A Difference of WMA & EMA on a sinusoid becomes superposed?

This is about signal processing, moving averages & superposed / standing waves. This is an online system: causal (univariate) time series analysis. Suppose you have a sinusoid of period n (i.e. n=40, so its frequency is 0.025). If you calculate a "weighted moving average" (WMA) on this sinusoid...
9. ### Curve extrapolation: polynomial or Bézier?

I confess! :smile: I guess that I want to use it as an indirect predictor: a predictor for the length of the look-back window of another filter. Whether that is prediction or not is debatable/semantics. In my opinion trying to find the instantaneous frequency of a smooth curve by some...
10. ### Curve extrapolation: polynomial or Bézier?

Yes, probably related to http://en.wikipedia.org/wiki/Runge's_phenomenon']Runge's[/PLAIN] [Broken] Phenomenon? I am afraid that for online analysis, the FFT suffers from edge effect. Something else I had in mind was this: the linearly swept sine / chirp: ( a sinusoidal wave that increases in...
11. ### Curve extrapolation: polynomial or Bézier?

My goal is not to use this signal as a predictor on itself: the data is only stationary, not periodic. I try to get an estimate for the instantaneous frequency of the smooth curve. This I can further use as an input for other filters and models that are calculated on the original signal so I can...
12. ### Curve extrapolation: polynomial or Bézier?

On a stationary, non-periodic signal (black) a smooth causal filter is calculated (green/red). It is sampled discretely (every distance unit of 1 on the X-axis). My goal is to find which "path" it is "travelling" on so I can extrapolate the current shape until it is completed (reaches a...