I am doing the following question (it is not homework, I am preparing for an exam).
The time discrete signals $x_1(n)$ and $x_2(n)$ is created by sampling the continuous signal $x_a(t) = \cos (2 \pi 300t) + \cos (2 \pi 600 t)$ with sampling frequency $F_s = 1000\textrm{ Hz}$, $x_1$ with anti aliasing filter and $x_2$ without aliasing filter.
- a) Calculate $X_a(f)$ for the time continuous signal $x_a(t)$.
- b) Calculate the magnitude spectrum for the time discrete signals $x_1(n)$ and $x_2(n)$ i.e $\lvert X_1(f)\rvert$ and $\lvert X_2(f)\rvert$, with $-1<f<1$.
I have done a), I used the table for Fourier Transform to conclude that $$X_a(f) = \frac{1}{2}\Big(\delta(f+300) + \delta(f-300) + \delta(f+600) + \delta(f-600)\Big).$$
But I can not solve b), I believe that I can use the information/answer from a) that is why I provided it.