Ideal reconstruction after down sampling The signal $x_a(t) = \cos(2\pi450t)$ is sampled.

F = 450
Fs = 1000 Hz
f = F/Fs = 450/1000   // Sampling theorem is fulfilled
x(n) = cos(2*pi*(450/1000))


The signal is then down sampled with a factor 3.

fNew = f*3 = 450*3/1000 = 1.35
xNew(n) = cos(2*pi*1.35)


Now the signal is prepared. How to make an ideal reconstruction using 1000Hz?
The signal can not be reconstructed because in the new sampled signal the sampling theorem is violated.  Aliasing would occur and the signal reconstructed would  be a lower frequency than the original signal.