Problem: The signal $cos(2\pi14100t)$ is sampled at $F_s = 400 Hz$. It is then upsampled with a factor 3 and then reconstructed ideally with a new frequency $F = 500 Hz$.
I now want to find the new signal that is created.
Incomplete solution: With the frequency before sampling $\pm 141000 Hz$. After sampling the normalized frequencies:
$f = \pm {14100 \above 1 pt 400} \pm k = \pm (35 + {1 \above 1 pt 4})\pm k= \pm {1 \above 1 pt 4} \pm k $ per sample
Interpolation with factor 3 yields the normalized frequencies:
$f = {\pm {1 \above 1 pt 4} \pm k \above 1 pt 3} = $ 3 frequencies $\pm k?$
I know how to solve it past that to get the final $F= \pm f * F_s$. I.e. $y(t) = cos(2\pi f_1t) + cos(2\pi f_2t) + cos(2\pi f_3t)$.
So my question is how do I calculate the 3 frequencies? Would greatly appreciate a simple solution and not just an answer so that I actually understand this.