# Nyquist theorem & collecting digital values

In summary, the Nyquist theorem is a fundamental concept in digital signal processing that states the sampling rate must be at least twice the highest frequency in order to accurately sample and reconstruct an analog signal. It is important in collecting digital values to ensure the fidelity of the digital representation and is applied in practical situations to determine the appropriate sampling rate. However, there are limitations to the theorem as it is based on the assumption of a band-limited signal. It is crucial in digital signal processing as it sets the minimum sampling rate required for accurate representation and is used in various applications such as audio and video compression, digital filtering, and data acquisition systems.
I have a digital transmitter from which I collect and save values from. How do I know if I must apply this theorem or not? My values seems fine..

Welcome to PF.

If your values are fine, why do you need any theorem? The purpose of your question is unclear.

But if I guess, you are asking when sampling rate becomes significant. It is significant whenever the analog signal has frequency components higher than roughly 0.1 of the sampling frequency. It causes seemingly false readings because of aliasing. To prevent that, we typically use an analog low-pass filter before sampling and call that the anti-aliasing filter. Are you familiar with those concepts?

berkeman
Thank you.
Yes I have heard about them. But is this theorem the same for digital signals?

anorlunda said:
If your values are fine, why do you need any theorem? The purpose of your question is unclear.

The values differ at bit but I think it depends on some error sources. I just want to make clear that it’s not because of the sampling rate.

There's a contradiction. Normally we don't sample digital signals such as Ethernet.

I have a digital transmitter from which I collect and save values from. How do I know if I must apply this theorem or not? My values seems fine..

Note that there is no such thing as a "digital" transmitter in this context; real-world signals are always analog and will therefore have some (analog) bandwidth; meaning the theorem always applies.

Hence, you need to figure out the analog BW of your signal (or to be more specific. how much BW you need to capture the information you are interested in); and then make sure you are sampling at twice that rate if you want to be sure that you are capturing all the information. .

sophiecentaur
I have transmitters connected in serial on a bus network. The signals are transferred via usb/rs-485 converter. A single transmitter has the max sampling rate of 16hz. Together I can only sample with max approx. 1.6Hz. The serial baudrate is 9600.

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anorlunda said:
There's a contradiction. Normally we don't sample digital signals such as Ethernet.
Actually, the instant at which the decision is made about the digital value of each symbol totally involves 'sampling'. The analogue value of any digital signal at any time can consist of contributions of many other symbols - hence the principle of sampling in the middle of an 'Eye'. That technique has long been superseded by modern signalling systems which use some very fancy filtering over many symbols.
@linki You do not specify the coding and modulation system that you are using so I guess it will be a fairly straightforward one. You can rely on the basic rules of thumb for that but the sampling of some signals can involve a significantly lower sampling rate than the maximum frequency in that signal. Sun-Nyquist sampling can be extremely good value when the sampled signal has a degree of 'order' in its spectrum. You can sometimes arrange for the alias signals to fall between a comb of wanted frequencies in a signal. Spectrum space can be a limited asset and needs to be used 'intelligently' sometimes.

The acquisition is made in Labview using the Modbus library.

You need to add a anti-aliasing filter with a roll-off at half of the sampling frequency of the ADC

anorlunda said:
Welcome to PF.

If your values are fine, why do you need any theorem? The purpose of your question is unclear.

But if I guess, you are asking when sampling rate becomes significant. It is significant whenever the analog signal has frequency components higher than roughly 0.1 of the sampling frequency. It causes seemingly false readings because of aliasing. To prevent that, we typically use an analog low-pass filter before sampling and call that the anti-aliasing filter. Are you familiar with those concepts?

cabrera said:
You need to add a anti-aliasing filter with a roll-off at half of the sampling frequency of the ADC

As f95toli eluded to, you actually need a bandpass filter whose bandwidth is <1/2 sampling freq. Actual center frequency of the AAF is theoretically not important.

sophiecentaur
the_emi_guy said:
you actually need a bandpass filter whose bandwidth is <1/2 sampling freq.
Depending on the actual spectrum of the data (I'm thinking of comb spectra), you can be even more cheeky than that - as long as the artefacts can be guaranteed to lay between the elements of that comb spectrum. Early digital coding of good old PAL colour TV did just that and allowed some useful sub Nyquist sampling by choosing to make the alias components lie between the comb of line frequency harmonics. Perfect for stationary pictures but the artefacts would start to show when there was enough motion in the picture.

## 1. What is the Nyquist theorem?

The Nyquist theorem is a fundamental concept in the field of digital signal processing. It states that in order to accurately sample and reconstruct an analog signal, the sampling rate must be at least twice the highest frequency present in the signal.

## 2. Why is the Nyquist theorem important in collecting digital values?

The Nyquist theorem is important because it ensures the fidelity of the digital representation of an analog signal. If the sampling rate is too low, it can result in aliasing and distortion of the signal, leading to inaccurate and unreliable digital values.

## 3. How is the Nyquist theorem applied in practical situations?

In practical situations, the Nyquist theorem is used to determine the appropriate sampling rate for a given analog signal. This is especially important in fields such as telecommunications and audio engineering, where accurate representation of analog signals is crucial.

## 4. Are there any limitations to the Nyquist theorem?

Yes, the Nyquist theorem is based on the assumption that the analog signal being sampled is band-limited, meaning it has a finite highest frequency. In reality, many signals are not band-limited and can contain frequencies above the Nyquist limit, which can result in errors even with a sampling rate that meets the Nyquist criteria.

## 5. How does the Nyquist theorem relate to digital signal processing?

The Nyquist theorem is essential in digital signal processing because it sets the minimum sampling rate required to accurately represent an analog signal in digital form. It is used in various applications such as audio and video compression, digital filtering, and data acquisition systems.

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