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It is because the audio signals are real and already at baseband. In contrast radio frequency signals are often represented as complex numbers once they are brought back to baseband. Real signals can be represented as a single stream of real numbers, while for complex numbers two streams of real numbers are required to represent them (as in $I+jQ$).
When ...
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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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To complement @DanBoschen's answer: a real baseband signal is a purely in-phase signal. Its quadrature component is zero, so there is no need to sample it or represent it in any way.
An interesting approach, though, would be to represent a stereo signal as quadrature. You could define the right channel as the in-phase signal, the left channel as quadrature, ...
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Zero padding a signal in time domain will not increase resolution in the frequency domain. Consider N< M, It may seem that increase in length by zero padding (adding M-N zeros) increases the resolution, but it simply is observing the original N DFT coefficients interpolated by lagrangian interpolation and now observing this interpolation at M equally ...
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I would recommend a different approach without zero padding.
Choose your DFT frame sizes based a common time duration and do different sized DFTs on your different signals with a 1/N (or 2/N if you prefer) normalization factor. The rationale for this is that the bins in a DFT correspond to frequencies in units of cycles per frame making the same bin index ...
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Fft normalization is often an overlooked topic and many articles dealing with FFT just say to divide the fft ouput by N (divide by either N or N/2 depending on the actual
FFT algorithm used).
Real FFT usually discards the upper part of the spectrum (due to FFT redundancy) so the normalization coefficient here is N/2, rather than N.
So, my question is: ...
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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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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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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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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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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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