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I ended up with a quite satisfactory solution, not by using a Kalman filter, but by using the Savitzky-Golay differentiating filter. The algorithm is described more or less like this: In a for loop, apply a running window to get a segment of the unfiltered volume signal around a range of given time instants, as measured by the load cell; For each segment, ...


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Some remarks. The series in Eq. 1 of the question: $$y_m = \sum_{k=-\infty}^{\infty}\sum_{n=0}^{N-1}\operatorname{sinc}\left(\frac{Nm}{M} - n - Nk\right)x_n$$ explicitly means this (see this answer to the Mathematics Stack Exchange question: Notation of double-sided infinite sum): $$\begin{align}y_m &= \lim_{K_2\to\infty}\lim_{K_1\to\infty}\sum_{k=-...


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RMS is essentially a three step process on a signal: Square it, mean it, root it. Squaring is not so difficult in software. Two things to keep in mind here. First, squaring fixed point data will double the data width, so make sure you have enough precision to avoid overflow. Second, squaring a signal will double its bandwidth. Make sure you have enough ...


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FYI: This was the question I put to the math guys, but here I changed the notation from what might be most conventional to the math guys to one that is more conventional to EEs. (I am using that post as a starting point to sorta exhaustively deal with Olli's question, but in mathematical terms that are easier for me to grok, so i am not exactly following ...


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Depends on how long you sample. If you sample for any duration shorter than infinite, then you must sample at a rate higher than twice the bandwidth or twice the highest frequency for a contiguous spectrum baseband signal. HIGHER Also note that a non-zero amplitude infinitely long sinusoid at exactly half the sample rate would have infinite energy, e....


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You've got your answer but let me summarize a bit about your confusion. We can classify signals as being baseband (aka lowpass) or bandpass. The basic form of Nyquist-Shannon sampling theorem involves bandlimited baseband real signals and says that : A real, bandlimited to $W$ (Hz), continuous-time signal $x_c(t)$ can be exactly and uniquely recovered ...


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Well, according to Nyquist-Shannon theorem you should sample at a rate which is at least twice the highest frequency you want to capture. This is also referred to as the sampling theorem because it "forms the basis" for sampling. Now regarding your specific question, I have to say that cos(4*pi) (along with the rest of the components) is just a number which ...


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I'm top-editing this since it answers the question directly. The sinc series is fundamentally a $C/x$, so you can extract as many absolutely convergent series out of it as you want, but what is left over is still only conditionally convergent. Also, you can rescale $x$ and it is still a $C/x$ series. Saying you have a summation to or from infinity is an ...


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I try to think of it this way: In the time domain, when downsampling occurs, the signal gets compressed; while on upsampling, the signal gets stretched. Then, from the Fourier transform we know that time stretching means frequency compression, and vice-versa. It may not be a rigorous answer, but hope this helps!


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First off, you should realize that the FFT is just an efficient implementation of the DFT. Power of two sizes are the easiest for it, but modern implementations have slick tricks to do other sizes. Leave that up to the library. The results will be the same. If your peaks are sufficiently well spaced (two or three bins apart) the following article will ...


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