# Why is it better to sample white noise in frequency domain here?

We have a channel $c(t)$ that we want to sample. It can be expressed as $c(t)= g\ast x(t)$ where $x(t)$ is white complex Gaussian noise and $g(t)$ is a function that we know the PSD of, let's call it $G(f)$.

So two options if we want to generate samples of the channel response:

1. Let $g(t) = \mathcal{F}^{-1}[G(f)]$, then generate white noise $x(t)$ and let $c(t) = g\ast x(t)$
2. Since $C(f) = G(f)X(f)$, we instead generate the white noise $X(f)$, mulitply $G(f)$ and $X(f)$ and let $c(t) = \mathcal{F}^{-1}[C(f)]$

Apart from complexity issues, I wouldn't guess these methods would be too different. But at least for the PSD I tried it for (the Clarke's spectrum bathtub shape), there definitely was a difference at least when the number of samples $N_s$ was small. Sampling in frequency domain was better for small $N_s$. For large $N_s$ it didn't seem to matter.

So my question is, why does it matter? Does it have anything to do with my PSD getting asymptotic around the edges and that this will not be noticed when sampling?

• Will answer my own question, I think I figured out why this is the case – Benjamin Lindqvist Feb 4 '16 at 9:00