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From a slightly less "dsp-like" point of view, slightly more geometric / time series, but this also works: The relation between the sinusoid (of amplitude 1) and the unit circle is well known. Instead of thinking of a moving average as a geometric mean on a window that slides from left to right over the time series, you could also define it as the ...


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This would be trivial to do as simple decimation where each block increments its samples by $n+4$ with each block starting at sample 0,1,2,3 respectively. This is common with polyphase filter implementation and similar techniques to reduce the overall clock rate requirement for the processing (parallel processing). For more details on both of those ...


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Below is the analytic result for both the actual max value of $0.901243$ and the maximum value found by the OP of $0.898464$ The reason you are not getting the predicted maximum is your samples of the sine wave are not located exactly at the peak. This is clear if you zoom in on the plot and compare the two peak locations for the number of samples given (as ...


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Puzzle solved, thanks to Cedron Dawg and Dan Boschen! First, I ran a simple N point moving average of a sinewave, using the simulation model below: I used the OP's values: N = 10, P = 40, sinewave amplitude = 1 and a simulation step size, $\Delta t$, equal to unity. The results, shown in the next figure, are the same as those of the OP: The maximum ...


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Okay, this takes a bit of algebra, Euler's formula, and the geometric series summation formula, and some plugging and chugging, but here is how you can calculate it directly: $$ \begin{aligned} x[m] &= \frac{1}{n}\sum_{k=0}^{n-1} A \cos \left( (m-k) \frac{2\pi}{p} + \phi \right) \\ &= \frac{1}{n}\sum_{k=0}^{n-1} A \left[ \frac{e^{i\left( (m-k) \...


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The amplitude reduction is simply given as the magnitude of the transfer function of moving average filter. A moving average filter has a rectangular impulse response so the transfer function will be a $sinc()$ function. You need to sample the $sinc()$ function at the frequency or your sign wave


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For a sampled audio waveform (at least destined for human ears), any DC will typically be removed acoustically, electrically and digitally, and what you are left with is a nominally symmetric waveform (speech can have some asymmetry) fluctuating between +A and -A. For «loudness» you want to take the absolute value or square for a power estimate and do some ...


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What do these values actually mean? Are they arbitrary? Yes, pretty much: they will just be the scale of numbers your system works with. In floating point systems, we often see that samples get normalized to [-1,+1], whereas in fixed-point system, it's often things like [-2⁻¹⁵,+2¹⁵-1], depending on the bit width of the samples to begin with. So, this is ...


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