The signal $xa(t) = cos(2*pi*450*t)$ 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 $x_a(t) = \cos(2\pi450t)$ 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 xa(t) = cos(2pi450*t) is sampled.

F = 450 Fs = 1000 Hz f = F/Fs = 450/1000 // Sampling theorem is fulfilled

x(n) = cos(2pi(450/1000))

The signal is then down sampled with a factor 3.

fNew = f3 = 4503/1000 = 1.35

xNew(n) = cos(2pi1.35)

Now the signal is prepared, how to make an ideal reconstruction using 1000Hz?

The signal $xa(t) = cos(2*pi*450*t)$ 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?