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while converting analog signal to digital equivalent,we have a process that is called analog to digital conversion and it has two main steps/stages sampling and quantization? I am confused whether y axis is discretized in sampling stage along with x axis or only y axis is dicretized in quantization stage since x axis is already discretized in sampling stage?

Initially i thought that sampling only involves discretization of x axis but now i was watching following youtube lecture where it tell at approximately between 10 min and 11 min that discretization of both x and y axes are done during sampling stage?

https://www.youtube.com/watch?v=xUCsfKA8bi0&list=PLm_MSClsnwm9I2iviE0YKt6PZTyQCYc8j

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Sampling is the process of making the x-axis (time) discrete and quantization is the process of making the y-axis (magnitude) discrete. You can sample without quantization (such as done with an analog sample and hold circuit). Quantization is introduced through rounding or truncation when the sampled analog signal is mapped to a digital representation.

Analog to Digital Conversion

Sampling only causes aliasing distortion to the signal; if there is no energy above the half the sampling rate for real signals with real sampling, or above the sampling rate for complex signals with complex sampling, absolutely no distortion occurs assuming a perfect sampling clock with no hitter/phase noise (both aspects are not physically possible to totally eliminate but can each be reduced to below our level of concern).

Many A/D's, such as successive approximation converters, are implemented with a fast analog sample and hold so that the sampled signal is held while the conversion to digital takes place.

Quantization noise adds noise to the resulting signal, well approximated in most conditions as a uniform white noise: the noise distribution in magnitude is uniformly distributed over the magnitude of a quantization level and is white in frequency to the extent that each sample of the noise is independent of the next.

From that approximation of the noise we can arrive at the SNR estimate for a full scale sine wave to be 6.02 dB/bit + 1.76 dB, which we can increase further by “over sampling”; since the noise added is white, we can filter out the noise in the band we don’t need.

I have detailed that process further at this post: What are advantages of having higher sampling rate of a signal?

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Quantization and sampling are different things and they are treated mathematically very differently. However they usually happen both at the same time.

Anything represented "digitally" (i.e. as a series of numbers in a computer or a digital storage device needs to be both sampled and digitized. This is typically done with a process called Analog-to-Digital conversion, which does both in one step.

The reverse is Digital to Analog Conversion which produces a signal that's both continuous in time and in amplitude.

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  • $\begingroup$ you haven't mentioned explicitly about my query?whether y axis is discretized in sampling process along with x axis or only y axis is dicretized in quantization stage since x axis is already discretized in sampling process? $\endgroup$ – engr Jan 12 at 15:53
  • $\begingroup$ very often dsp literature and resources mentioned both these two process sampling and quantization separately on block diagram of ADC $\endgroup$ – engr Jan 12 at 15:54
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It’s helpful here to understand that there are two things involved with digital sampling: Of foremost importance is the sampling; secondarily, subsequent digitization allows us a number of conveniences.

That is, sampling theory does not require digitizing—you can store the analog levels obtained by sampling a signal whose spectrum is below half the sample rate. Play it back by running the samples as analog impulses, at the original sample rate, through a lowpass “reconstruction” filter set just below half the sample rate. You can even perform signal processing on the analog samples before the reconstruction filter, such as an analog multiplier to control gain.

If you’ve even seen or used an analog delay guitar pedal, that’s how it works. But you also might know that fidelity is not great, because it’s not easy to retain the analog values without degradation, resulting in noise and loss of high frequencies. And more advance signal processing in the analog domain can be costly and difficult to implement.

But if we digitize those samples, we are assured that they retain their values without change for an indefinite amount of time. And if we store them in a numerical processor, we can use many advanced digital signal processing techniques on them, limited only by the processor speed.

One of the few concessions we must make is that we need to decide on the digital precision we use to obtain and store the digitized values. Fortunately, we’ve been able to get very good precision, affordably. Limits of the human ear and electronics (thermal noise is unavoidable above absolutely zero) run around 20 bits, and we usually support 24 bits mostly because it’s an even byte above the minimum we accept as high-quality (16-bits), and allows for additional headroom.

So, sampling is what you referred to as the X-axis, the time axis. Here you’re mainly talking about long-term clock accuracy and jitter, both of which we’re very good at. We rarely have to worry about this, and it’s not something that normal signal processing algorithms can affect. So while sample rate is an important consideration for bandwidth, maintaining it is not an issue.

And the Y-axis is essentially the digitization accuracy. We’re also very good at that, but in our digital signal processing algorithms we need to take care that we aren’t degrading the level we already have, by neglecting quantization effects that can grow with poorly designed algorithms. Quantization effects are one of the major points that DSP coders need to pay attention to.

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