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this post was submitted on 16 Jul 2023
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Showerthoughts
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"Didn't understand the sampling theorem" for $2 please.
As long as the frequency of the measured signal is <1/2 the sample rate, you can reconstruct the original signal perfectly.
If you plugged this jaggy-looking graph into a digital to analog converter with perfect analog circuitry, you'd get exactly the sine shown.
I think parent is referring to quantization in the amplitude/y-axis (bitdepth), whereas you are referring to quantization in time/x-axis (sampling rate).
Quantisation is a potential factor but the graph does not show its effects and their comment describes the supposed effects sampling, not quantisation.
Also, when we come to discussing SNR, you'll have to consider the SNR of analog systems too.
Pardon me? The blue graph is obviously a result of sampling and quantization of the red graph. If there was no quantization but only sampling going on there would be exclusively vertical blue lines with precise values instead of quantized values and no horizontal blue lines because no data between samples. To be precise, the blue graph does not even show the precise values of the samples but only the results of the quantization of those. Exact sample values are only indirectly in this graph - they are where red graph and blue vertical lines meet.
However - I was primarily referring to OP´s idea that digital speedometers would be more precise than analog speedometers. If you look at the graph you will see that the analog speedometer always knows and thus displays the exact speed of the car in any moment (plus a small inevitable speedometer system delay). The digital speedometer on the other hand most of the time only knows the quantized value of the last taken sample - except in the exact moments when the samples are taken. Considering the quality (resolution and speed) of nowadays digital technology I assume this is not a factor to consider when designing speedometers though.
The graph posted absolutely exhibits both quantization and discrete sampling. The blue trace on the Y-axis shows steps of 1
that's quantization.
I should have been more clear: The negative effects of quantisation. Obviously sampling into discrete values is shown but not the negative consequences that can have.
A DAC interpreting the blue trace will output something extremely close to the red one. There might be a slight bit of error in it due to the quantisation before but the graph does not show that and it probably couldn't since it'd be so tiny. A good way to show quantisation noise would be a histogram with a signal in the middle and some quantisation noise around it.
The DAC would not output the jaggy line. It couldn't, that's not a valid analog signal. Painting the steps between the points can be done if your audience knows what that means but can be extremely misleading if it doesn't. Those lines between the points with 90 degree angles don't exist in the real world, they're just interpolated between the points in the visualisation.
A much better way to represent digital samples in such a chart is the way it's done in the wikipedia article on the topic: https://en.wikipedia.org/wiki/Sampling_(signal_processing). They're just discrete points. If you did the same interpolation between the points as a DAC would do (which is not nearest-neighbour interpolation), you'd get the analog trace shown.
Interesting. Does quantization not always refer to quantization of the amplitude value of a sample while the sampling rate is always referred to as the ... sampling rate? I get what you mean by quantization of time but I have never heard anyone calling the sampling rate that before, so now I´m asking myself if it even is a real quantization because there is no value approximation going on and the sampling frequency is an exactly known value at all times.
Yes I think you used the terms correctly
it should be referring to the amplitude. "Discrete sampling" or just sampling rate is the preferred way to refer to time, you're right.
I was trying to use consistent language in response to the reply claiming you were misunderstanding the sampling theorem. I think that poster was confusing discrete/quantized steps in time with discrete/quantized steps in amplitude.
Their comment about SNR is certainly true though.