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When converting an analog signal to the digital domain I understand that one does two things.

  1. An analog signal is continuous and must be sampled in to discrete time segments (Discretization)
  2. The analog signal ideally represents the true value but in the digitization must be quantized to specific values in our system (Quantization)

Is it possible to have one without the other, if so in what context? I hope i'm being clear with my question.

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When we talk about a digital representation of a signal it is implied that we can store this representation in memory, which requires that the amount of information (bits) is finite.

An analog signal has an unbounded amount of information, both in its level and in its variation in time. To make the amount of information finite you must quantize both.

Both 'single dimensional' quantizations you suggest can be done, but each transforms an analog signal into another analog signal, that must undergo further quantization before it can practically be converted to digital.

Brain mentioned an application of discrete-time continuous-value. A LED bar that indicates the loudness of your music is an example of an (in principle) continuous-time discrete-values system.

One could argue whether a continuous signal in either dimension exists at all. Charge is quantized (number of electrons) and according to modern theories time is so too, and practical circuits have limited speed anyway.

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  • \$\begingroup\$ Thats an interesting way to think about it, Discretization is simply Quantization in the time domain? Do you think you could give me an example of a Quantized non discrete signal, as the other answer says such a think is not possible? \$\endgroup\$ – secretformula Feb 12 '14 at 19:05
  • \$\begingroup\$ I don't fully agree with your wording, IMO discretization does not imply that it works on the time domain. But I think we agree on the concepts. \$\endgroup\$ – Wouter van Ooijen Feb 12 '14 at 19:07
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A discrete time signal is just a sequence of numbers. They could be real numbers, mathematically.

If they're in a computer, they need to be represented somehow, and that representation means that they can't be infinitely precise, however they can be arbitrarily precise. If you wanted to represent the diameter of the universe (~\$10^{11}\$ light years) with a resolution of one Planck length (~\$1.6\times 10^{-35}\$m), you'd need about 61 digits. No problem with a computer and appropriate software, just ask for it.

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  • \$\begingroup\$ See the bottom table in the link in my comment up above. \$\endgroup\$ – Ignacio Vazquez-Abrams Feb 12 '14 at 23:04
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A regularly clocked sample and hold discretizes a signal in time, but retains the continuous voltage.

The other way around is not possible since quantized values are inherently discrete.

Added:

I see some disagreement about a signal quantized to a set of levels being inherently discrete in time.

Let's consider what such a quantized but continuous time signal would have to look like. Quantized means that the signal level is expressed as a number at any one instance in time. To not be quantized in time, this number must reflect every change of the input value crossing between quantization domains. This is simply not possible as it requires infinite bandwidth.

Consider the simplest quantization scheme of all, which is a 1 bit A/D, also known as a comparator. The input signal is quantized to only one of two states. To be continuous in time, the comparator would have to respond to every possible excursion of the input signal accross the boundary between the two quantization domains. However, any real comparator will some length of excursion that it will not reflect on its output. The comparator will be "blind" to the input signal crossing the threshold for some minimum time after it responds to a change. Put another way, to not discretize the input would require infinite bandwidth, which is not physically realizable.

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  • \$\begingroup\$ The other way around is not possible since quantized values are inherently discrete. That is most certainly not correct. A good example would be an ideal DAC. Discrete time implies that the value is known only in certain time points, while with an ideal DAC, we have limited set of amplitudes available but there is a voltage value in every time point. \$\endgroup\$ – AndrejaKo Feb 12 '14 at 19:12
  • \$\begingroup\$ @Andrej: But this ideal D/A of yours would have to have infinite conversion rate, which isn't possible. Any finite conversion rate implies samples at discrete times. Even the limiting case of a 1 bit D/A (comparator) will have some finite propagation delay and some maximum frequency its output can ever produce. \$\endgroup\$ – Olin Lathrop Feb 12 '14 at 19:18

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