This is a very applied question, but I hope it belongs here.
When you do numerical integration, you introduce some error, for example in the trapezium rule you cannot have infinite trapeziums, and so this has some error relating to the number of trapeziums you choose to approximate it with.
Now if you look at the following property we can represent integration in the Fourier domain as
$$F_k[x(t)] = \frac{F_k[v(t)]}{2\pi i k}$$
So in the time domain on the LHS the error of integrating velocity depends on the number of trapeziums for example (or whatever method you are using). How can the error of the integration be approximated from the RHS? Does it depend on the frequency resolution, or the $N$ sinusoid basis functions, or is it something else?
$$F_k[x(t)] = \int_{-\infty}^{\infty} x(t) e^{-2\pi i k t} dt $$ where $k$ indicates the frequency of each sinusoid, x(t) is a displacement signal, v(t) the signal in velocity