I have a function with an equation:
$$C = 1.6925\left( e^{-0.136t}-e^{-1.192t}\right) $$
Where $C$ is real and $t$ represents time in hours. Beneath is the representation of my function.
I am trying to find the best sampling step (based on Nyquist-Shannon theorem) to sample and reconstruct this function using a Fourier Transform.
After using a Fast Fourier Transform algorithm in MATLAB (fft
), by setting:
x= fft(c);
xmag=abs(x); (amplitude estimation)
I find the below spectrum for the function for a $t$ between $0$ and $100$ sampled at $1000 \text{Hz}$ , with the highest amplitude at:
bin(1) = 1.1025e+04
and the second highest at bin(100001)
with an amplitude of 9.9946e+03
. the bin number 100001
represents also the length of xmag
.
So my question is how would you interpret the spectrum? Specifically I would like to know how to determine the highest frequency at which I can sample this function and reconstruct it without aliasing?