# Estimating the Nyquist rate when simulating data

I want to find the power spectrum $\tilde{Q}(\omega)$ of a quantity $Q(t)$. The values of $Q$ are computed at discrete time steps so I have a series $Q(\Delta t)$, $Q(2 \Delta t)$, ... of values, but the calculation at each time step is independent rather than (for example) needing to know the value of $Q(\Delta t)$ in order to compute $Q(2 \Delta t)$. I then compute the power spectrum of $\tilde{Q}(\omega)$ by an FFT of the signal.

My main question is what is a good way to choose $\Delta t$ i.e. estimate the Nyquist rate of $Q(t)$ without wasting a lot of computing time?

I'm also wondering, given that the calculations at different times are independent, is there a smarter or more efficient way to find $\tilde{Q}(\omega)$ than generating a time-series and performing an FFT.

• Hi! What is the method (or simply the formula if there is any) that you use while computing the samples $Q(\Delta t)$ of $Q(t)$ ? Or stated in signal processing terms is the signal $Q(t)$ band limited? If so what's its bandwidth? – Fat32 Feb 28 '17 at 15:49