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Suppose I have some data vector, $\mathbf{d}$ with length $N$. I want to add "Gaussian noise" to the data. My understanding is that there are two ways to do this.

1) Relative noise percentage

$$\mathbf{d_n} = \mathbf{d}+\epsilon\mathbf{dr}$$

where $\mathbf{d_n}$ is the noisy data, $\epsilon$ is the error fraction and $\mathbf{r}$ is a vector of numbers drawn from the Gaussian distribution.

2) "White" noise

$$\mathbf{d_n} = \mathbf{d}+\xi\mathbf{r}$$

where $\xi$ is the "noise floor".

In the first scenario, the added noise is dependent on the data itself (i.e. a large data value will likely have a larger noise term than a smaller data value). In the second scenario, the noise is independent of the data.

Which is "better"?

Why choose one method over the other?

Any information is appreciated.

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