# Power spectral Density after Sampling

I'm working in a project where I need to identify the noise features in a signal coming from a sensor. Suppose to call the noisy signal as $y(t)$, we define its components as

$y(t) = y_{true}(t) + w(t) + b(t)$

where $y_{true}(t)$ is the deterministic signal, $w(t)$ is a white noise with power spectral density $S_w(f) = A$, and $b(t)$ is a Gauss-Markov process with PSD $S_b(f) = \frac{2 \sigma_b^2 \beta}{(2\pi f)^2 + \beta^2}$ and correlation function $R_b(\tau) = \sigma_b^2 e^{-\beta |\tau|}$.

To identify all the parameters of the signals I'm using the Allan Variance (I will give you more information if someone is interested).

The signal $y(t)$ is sampled for a time $T$ seconds with a sampling time of $T_s$ seconds. I wondering how the PSDs of the noises change after the sampling. In general, how the PSD of a stochastic process change after a sampling?

Thanks a lots!

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