Using Discrete Fourier trasform of the samples of a continuous/periodic signal to obtain frequency data similar to FT of the original signal

Question

Suppose we have a continuous and periodic real-valued 1D signal $f(t)$. Let us say we obtain finite number of samples $f(n)$ from $f(t)$. Is there a way to take discrete Fourier transform of $f(n)$ and obtain data similar to $F(\omega)$, Fourier transform of $f(t)$? If this is possible, how do we convert discrete Fourier transformed frequency data into time format?

Answer 1

If the samples are equally spaced then the Fourier Transform coefficients $F(\omega)$ are the Discrete Fourier Transform coefficients.