Update Content - 2020-09-04
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@ -14,7 +14,7 @@ This analysis is taken from [here](https://www.allaboutcircuits.com/technical-ar
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Let's note:
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- \\(q = \frac{\Delta V}{2^n}\\) the quantization in [V] (the corresponding value in [V] of the least significant bit)
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- \\(q = \frac{\Delta V}{2^n}\\) the quantization in [V], which is the corresponding value in [V] of the least significant bit
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- \\(\Delta V\\) is the full range of the ADC in [V]
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- \\(n\\) is the number of ADC's bits
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- \\(f\_s\\) is the sample frequency in [Hz]
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@ -23,9 +23,9 @@ Let's suppose that the ADC is ideal and the only noise comes from the quantizati
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Interestingly, the noise amplitude is uniformly distributed.
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The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution).
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Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#org5158d30)).
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Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#orgf06d261)).
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<a id="org5158d30"></a>
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<a id="orgf06d261"></a>
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{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
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