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Yes that is correct. The width of the transition band is inversely proportional to the length (or memory) of the filter which means to say that you would need an infinite amount of time to achieve your perfect filter. Therefore for practical reasons you decide how much aliasing would be tolerable (similar in many ways to deciding how many decimal places you ...


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Your plot is correct. You are sampling three waves $f_1 = 10\textrm{Hz}, f_2 = 30\textrm{Hz}$, and $f_3 = 70\textrm{Hz}$, with a sample frequency of $F_s = 1.5\times70\textrm{Hz} = 105\textrm{Hz}$. This means that your Nyquist frequency is $F_N = F_s/2 = 52.5\textrm{Hz}$, and corresponds to the maximum value of your frequency axis. As such, the signals $...


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Sound absorption is an example of filtering. You can build an enclosure (room) to lessen sound coming from your clothes washer. Adding insulation inside the wall helps further, as does offsetting studs on each side to minimize vibration transfer. This comes at a cost, but at some point you’ve made the problem unnoticeable—you don’t need 100% eradication. ...


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I don’t think that you can do multi-frame super resolution in the traditional sense if there is no camera rel scene movement, nor if the camera applies «proper» Nyquistian spatial prefiltering? I think of good old interlacing as an example of potential super resolution. You get a 2-frame cadence consisting of separate time and spatial samples, usually ...


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Your premise is due to the physical nature of the device under test it is possible that occurrence of higher frequencies vibrations can be predicted by lower frequencies and this is important as it will allow you to use a lower bandwidth sensor that can only respond to lower frequencies. Interesting problem and I would suggest this approach to find evidence ...


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does aliasing occur always if i sample a vibration in real world applications? Yes. The aliasing always occurs. The sampling theorem assumes band limited signals, but these strictly band limited signal do not exist in reality (as they would be infinitely long). Of course any signal can be low pass filtered to be reduce the aliasing to an acceptable level ...


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If I have a vibrations sensor that has a max sample rate of 8kHz -> It can reconstruct signals till 4kHZ perfectly right? Theoretically, yes. Though I would like to add that all the noise signals beyond $+/-4kHz$ will alias back into your sampled signal. But what about frequencies which occur also in the measurements with much higher frequencies? If ...


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That is why, before sampling, a (steep) lowpass filter with cutoff frequency $f_c \leq \frac{f_s}{2}$ shall be applied. Thus, the amount of aliasing will be insignificant.


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