11

Oversampling means to sample at significantly more than the Nyquist Rate. When using an ADC, the ADC generates quantisation noise because the continuous valued signal has to be translated to discrete output values. If you oversample then this noise power is "spread out" over a larger frequency range, i.e. it has a lower spectral density. So if you apply a ...


8

The minimum sampling rate needed is twice the highest frequency of the spectrum of the signal you wish to measure. If the highest frequency in the spectrum of the signal is 10kHz then you need to sample at least twice as high (20,000 times per second) in order to avoid aliasing. Most folk go a bit better than this and, for instance, CD's sample audio at 44....


6

I was under the impression that the FFT was inherently calculated at every frequency 0->(Sampling Frequency)/2 distributed in bins of width Fs/(2*N). This is roughly correct. A discrete fourier transform (DFT) produces output for frequencies between \$-F_s/2\$ and \$F_s/2\$. If the input data is real-valued (rather than complex) the negative-frequency ...


5

You can't reduce noise that is already present at base band but, by appropriate filtering and over-sampling you can reduce out of band noise aliasing into the base band when the ADC converts. Aliasing: - Here, a signal (in red), is grossly under-sampled and it produces the blue signal. The blue signal is not representative of the original red signal and ...


5

Since your ADC is already more than fast enough, it would be far better to do all of the filtering, decimating, averaging, etc. that you're talking about in the digital domain, rather than in the analog domain. Then all you need in the analog domain is a low-pass filter that meets the antialiasing requirements of the ADC's actual sample rate. EDIT: OK, I ...


4

You are right that the FFT computes equidistant frequency samples over the whole frequency range. Apart from the Goertzel algorithm mentioned in The Photon's answer, you could also use the Chirp Z-transform, which allows you to zoom in on a certain frequency range. This document explains the algorithm and it also contains a Matlab implementation (which is ...


4

It won't vary with input signal level the way you've shown it, however it will vary with impedance of the source. I suggest adding the noise with an op-amp to isolate the input from the noise source. You should probably have an anti-alias filter on the input signal before adding (unless it's naturally band limited) and make sure that the input is not ...


4

Frequencies work differently than that. As pointed out in the comments to your question, your noise will just alias into the bandwidth you do have. Aliasing means that a frequency you should be seeing gets interpreted as a lower frequency because your bandwidth isn't large enough. The nyquist frequency is intended to determine what you will be able to see/...


3

Your college does not seem to remember her statistics lessons. The additional higher frequency noise can be trivially filtered with a low pass filter, and the filtered signal might be better than one sampled at low frequency (oversampling). Note that using a standard oscilloscope to record live ECG violates patient protection, as medical equipment requires ...


3

I see quite a few misstatements and possible misconceptions both in the answers and in the question, so let’s break down what is meant by “noise.” Analog noise within the same bandwidth as the signal. Analog noise outside of the bandwidth of the signal. Quantization noise introduced by the ADC. I interpreted your question as implying option 1. ...


2

The DFT (discrete Fourier transform) is a process that takes N samples of data in the time domain and produces N samples of data in the frequency domain. It requires on the order of N2 operations (this is written as "O(N2)") to complete the full calculation. Each of the N output values is computed independently, and each one takes O(N) operations to compute. ...


2

The quantity of bits are those actually present in the result, not the resolution. As such they should be >= the resolution. In other words, if the ADC has a resolution of 12 bits, the x2 oversampling gives you 0.5 bit more resolution but to report it you must use 13 bits. So the result with 4x oversampling is 'better' in terms of resolution than the 2x ...


2

Unless your signal has zero mean, I would avoid zeroing the missing samples because that would introduce bias in the estimation of the mean, the power and the spectrum of the signal. Instead, the best estimation of the missing samples is the average value of your time series. However, using the mean isn't good either. The subset of replaced samples would ...


2

The reference level for an ADC is the maximum signal that meets some quality criterion, for instance distortion. In an ordinary ADC, exceeding the rails results in a distorted signal. In a sigma delta ADC, exceeding the stability threshold results in a distorted signal.


2

However, once I've sampled at 160KHz, why would I want to apply a digital low-pass filter before decimation? What are the advantages of this? Aliasing, as a problem is not reserved purely for the analogue world - you also need to low-pass-filter it in the digital domain when decimating. The same rules apply - you need to restrict your bandwidth whenever ...


1

This answer is not exact but should help to provide at least a good intuition. In a word the answer is "decimation". As explained in this Maxim tutorial and other places, the front end of a delta-sigma ADC yields a 1-bit data stream: The output of the sigma-delta modulator is a 1-bit data stream at the sampling rate, which can be in the megahertz range. ...


1

First of all if your signal of interest is 50 Hz maximum then providing your sampling rate is greater than twice 50 Hz you don't need an anti alias filter. However, sampling at a higher rate does improve the ability to restore that signal back to an analogue waveform without loss of amplitude. Consider these two scenarios: - In the top picture a waveform is ...


1

No, it isn't true at all. Even if quantization noise is the only source of error in your system, oversampling allows you to spread that noise over a wider bandwidth, and noise shaping allows you to move most of the noise energy to a frequency band that you don't care about, improving the SNR in the band of interest.


1

You design the buffer amplifier to fit your signal, not the sampling rate of the ADC. But the buffer's output impedance has to match the ADC's input impedance requirements at the sampling frequency. As a side note: Oversampling will reduce noise (which the STM32 ADCs have a lot of) but not the non-linearities of the ADC. You will still get just 12bit ...


1

Can you please point out some reasons for this? For the ADC: - Zero offset error as specified in the data sheet Gain error as specified in the data sheet Integral non-linearity error as specified etc.. Differential non-linearity error as specified etc.. Plus you have a resistor tolerance in your potential divider and you have a measurement accuracy in ...


1

Assuming the PIC has an analog input capable of operating at 32MHz or significantly higher than 9kHz (Nyquist Frequency), then yes it is possible to use averaging to increase the SNR. It is important to consider the issues with respect to your SNR. For example, if the SNR is low due to transmission distance (attenuation), then averaging may not be very ...


1

My gut reaction is that if the overall signal mix extends to 20Khz, any under sampling trick you attempt to measure your embedded 200hz is not going to work. I think you're going to have to either properly sample at 2X or better (40Khz + ) and then apply fast Fourier transform techniques to extract and measure the 200hz, Or, since you're talking about a 100/...


1

Ten bit data can be increased in resolution if there is gaussian noise present and oversampling is performed. 4 times over sampling increases the resolution from 10 bits to 11 bits. 4 x 4 times oversampling gets you one more bit and 4 x 4 x 4 (=64) times oversampling gets you another bit. So with 64x oversampling you get 13 bits resolution from a 10 bit ...


1

If I read your question correctly you can decimate after your ADC and get resolution gains (as you can do with any ADC). For each additional bit of resolution to be gained, you decimate/average 4 samples so, 23.7k divided by 4 gets a decimated rate of 5.925k and the resolution increases from 19.5 bits to 20.5 bits. Decimate by 4 again and you get a sample ...


1

There are other reasons for over-sampling. First is if you want to reconstruct the signal back into the analogue domain you have an easier job designing the DAC output filter. Remember that the process of digitization does "corrupt" the signals closer to half sample rate and that corruptions lowers the higher frequency amplitudes by a few dB - the ...


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