Duration of downsampled signal in analog frequency axis

Question

Suppose, I sampled a signal, $x(t)$ and let $x[n]$ be the sampled signal of $x(t)$. Let then I downsampled $x[n]$ by a factor of $M=3$. Let $x[n]$ after being downsampled by the factor of $M=3$ yields $y[n]$.

Now, my question is: if I plot the frequency spectrum of $y[n]$ along y-axis with frequency (in Hertz) along x-axis, then, will I get only $M=3$ copies of frequency scaled version of the original spectrum(spectrum of the original signal, $x(t)$) or I will get infinite copies of the original spectrum ?

Answer 1

If you plot spectrum of y[n] along y-axis and frequency(in Hertz or in any other suitable unit) along x-axis, there will be infinite copies of the frequency scaled(by a factor of M) version of the original spectrum(i.e, spectrum of original signal x(t)) each around kFs, where k is an integer and Fs = sampling frequency.