# Power spectrual density of white Gaussian noise

I know that power spectral density of white Gaussian noise is $\frac{N_0}{2}$.

In a simulation I want to plot a system output and its very important to define the value of $N_0$,I want to know what is $N_0$ and its value?

• Um, your question shows your problem: "it's important to define $N_0$". Exactly. $N_0$ is the noise density, and you define it for your simulation. As simulations simulate a real system, you must describe the noise that this system sees, so that you can derive the noise density. – Marcus Müller Aug 19 '16 at 9:21
• Thanks dear Marcus , for a theoretical analyze how can define the N0? does it have any formula to assume for a simple calculation? (for example for ideal system ( for a white noise input signal and a narrow band pass filter) what can PSD be? – Ehsan Zakeri Aug 19 '16 at 10:02
• For a simulation, you must describe your system. Noise density is one of the crucial aspects of that description. It can take any non-negative value. – Marcus Müller Aug 19 '16 at 10:04
• That being said, you can always assume a baseline Noise density based on Johnson-Nyquist Noise, which would have a power density of $k_b T$. Add in estimates for the temperature of your system, and also don't forget that all active components have a positive Noise Figure. It's totally unclear what the values of these Noise Figures are, and estimating them is the central problem that only you, with knowledge of your system, can do. – Marcus Müller Aug 19 '16 at 10:07

$N_0$ is one of the characteristics of your system, you don't have to define it yourself but to know which is the one of the system you are using. A differente case would be if what you wanted was to see any kind of behaviour related to the $N_0$. In that case, you should just make a sweep in the value of this variable. As Marcus said, you can have a first aproach of the noise in your system using the Thermal noise.