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4

The author is modeling quantization noise as being white (i.e., each sample is independent of previous or following samples) with each sample being a zero-mean, uniformly distributed random number with a span of one: $$p(x) = \begin{cases}1 & -\frac{1}{2} < x < \frac{1}{2} \\ 0 & \mathrm{otherwise}\end{cases}. \tag 1$$ Do the math (or look it ...

5

In the case of uniform quantization, and under some light hypothesis for the signal, the error can be modeled as an additive IID signal, independent of the signal, and with uniform distribution between +/- half LSB. The power of such error is then $\Delta^2/12$, where $\Delta$ is the amplitude of one LSB. Taking the square root and calling it standard ...

10

I currently work in the design of atomic clocks and precision frequency sources and pleased to report that the Allan Variance is still quite relevant and useful. In fact it's utility extends to convenient characterization of many non-stationary processes, well beyond its primary tool as a frequency stability assessment. (And as mentioned in its comments, it’...

6

Your formulation: $$\arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \right\|}_{1}$$ Has 2 elements: The Fidelity Term This is basically measurements term with the model of AWGN with IID noise. The Regularization Term This is a sparse promoting model by using the Laplace ...

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