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We have a coherent and consistent theory of sampling that proves that band-limited signals can be sampled without loss of information.
We have a coherent and consistent theory of quantization that proves that quantization always creates an error
The question of "why" is meaningless. Things are what they are.
In any real world application you need ...
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A couple of intuitions. Small sample jitter over most of the band is equivalent to additive noise, (maybe) correlated to the signal. For non-ideal sampling, where out of band energy is non-zero, jitter has the beneficial effect of randomizing the sampling with the phase of repetitive signals, so rather than classical aliasing, the out of bands signals can ...
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B): $f_s \geq 2B = 2\cdot(2015-1612) = 2\cdot 403 = 806$.
"Second-order" bandpass sampling is described in this paper (or older, here). It's sampling $x(t)$ at a lower sampling rate, $M$ times, each with a different offset - then keeping only (carefully selected) 2 of the $M$ sequences:
$$
\begin{align}
x_A(n) &= x(n / f_0) \\
x_B(n) &= x(n ...
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A perfectly band-limited signal must have infinite support, thus must be infinitely long. A signal that can be sampled without error at any sample spacing of frequency below Nyquist, must have a value that is an exact integer multiple of your quantization spacing.
So I think the constraint required for both of your reconstruction theorems to hold only ...
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It may help to understand that a critical difference is time is not the independent variable when we are sampling. When we sample, we quantize time and at that specific sample location we then determine the dependent variable (which we can the quantize or not as a different process, sampling in time is independent of sampling in magnitude).
Specific to the ...
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Sampling theorem tells us we can sample only a band-limited signal. This means, the signal should have a maximum frequency with respect to time.
If a signal has a maximum frequency with respect to amplitude, we can apply sampling theorem to the amplitude as well.
In the sampling theorem, it is not necessary for the x-axis to be time for it to be applied. It ...
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