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.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..
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 That technique has long been superseded by modern signalling systems which use some very fancy filtering over many symbols.There's a contradiction. Normally we don't sample digital signals such as Ethernet.
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?
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.You need to add a anti-aliasing filter with a roll-off at half of the sampling frequency of the ADC
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.you actually need a bandpass filter whose bandwidth is <1/2 sampling freq.