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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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Sampling operation has its roots in the mathematical interpolation theory which was used to generate certain function values at specified points from the availabe set (the samples) of existing values. These kind of work is summarized as Whittaker interpolation. Lagrange interpolation is also another related concept. Sampling theorem in electrical ...


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OP here. (Looks like I changed my name from Oscar to Jerry.) Sorry for letting this go for so long. The correct answer to my question is that the use of the naked delta—including under non-limiting integrals—is a shorthand. Whenever you see a naked delta, you may replace it with some suitable limiting integral of a unit-area function that tends to zero ...


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One more possibility, if you have a lot more and longer training data than production data. Attempt to train a machine learning model (DNN, etc.) against shorter segments of the test data to predict the interpolated values in regions where Sinc interpolation alone is too inaccurate. Use data from longer segmenting to validate during training. If you don'...


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The achievable rms accuracy is approximately the reciprocal of the SNR as an rms quantity, specifically $10^{-35/20}$ in your case assuming the small angle criteria, if your noise is all phase noise. It is likely your SNR is equally phase and amplitude noise, so the phase result as limited by your noise would be 3 dB better after hard limiting the signal to ...


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Yes that is correct-- if you sampled the audio recording at 48 KHz and then played those same samples back at 44.1 KHz you would be "time-stretching" the recording and it would be slower. However you can also resample the samples by the ratio of 147/160 to then have the 44.1KHz samples play back at the same speed.


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You are right. If you play back your original samples at a lower sampling rate, the resulting signal will sound at a lower pitch, and will take longer to play. If you want to convert your original samples to a lower sampling rate (but keeping pitch and length, and losing a bit of bandwidth), you need to resample your signal. Most audio software, tools and ...


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One possibility is to use a "discrete sinc interpolation", which uses a compact support version of a sinc (which is not a truncated sinc). Otherwise there are methods based on the discrete cosine transform (DCT) and discrete sine transform (DST). Another interesting approach is based on "sinc-lets". These are reviewed in this paper. In particular, look at ...


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A bandlimited signal is infinite in duration. Even a low pass filtered signal for anti-aliasing implies a long duration. So if you don’t have signals off the ends, try generating them. Add a Monte Carlo shotgun of points to each end generated using anything known about the legal distribution of the signal. Reject the random end extension points that ...


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I think I have the gist of what you are asking, but I am clarifying to make sure. Short answer: Yes, using a DFT. You just have to compensate (select) the correct alias. The assumption is that your signal is a periodic one. Also that when you say "band limited", but the fundamental won't suffice, the signal is composed of the fundamental and a few ...


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I have some very short signals in the range of 8 to 16 samples. These represent a bandlimited signal, sampled at or slightly above the Nyquist rate. Nope. A signal can't be limited in time and in frequency at the same time. If it's very short, than chances are the bandwidth is a lot higher than you think it is and that you've already picked up some ...


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When generating the sine wave, the code uses a sampling frequency to establish discrete points in the time domain. It is not continuous. This means the wave is broken up into bins that are exactly 1/fs in size/width. So if you want a true integral of the wave, you have to take the average density of all the points in a bin by dividing by the sampling ...


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