# How to derive low pass filter $\frac{N}{N+S}$

I watched the video for PID control system where it mentioned the Laplace domain function and low pass filter to be $$\frac{N}{N+S}$$. I used asymptotic analysis to see that it made sense. However, I'm interested in how it was originally derived. How did Laplace domain function lead to the low pass filter?

• I am not sure that it is a minimal question. Can you edit the question in a way that does not require to see the movie in the link? – Gideon Genadi Kogan Feb 20 '20 at 9:33

I assume that you want to see that the transfer-function magnitude is inverse proportional to the frequency. In this case, you replace $$S$$ with $$i\omega$$ and you get that the transfer function magnitude decays with the frequency$$|G(\omega)|=\left|\frac{n}{ n+i\omega}\right|$$