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Let $x[n]$ a discrete-time signal, $$y[n]= x[2n]$$

I have seen that if $x[n]$ is periodic then $y[n]$ is periodic. Similarly, can we say that if $y[n]$ is periodic then $x[n]$ is periodic as well. Why, why not ?

NashEw.
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    No, the equation only constrains $x$ at even indexes. $y[\frac n2]=x[n]$ (integer division) would be different. –  Feb 26 '15 at 12:14

1 Answers1

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You can't say anything.

Suppose you have the signal $y[n] = 1$, it's periodic

Now you have the signal $x[2n] = 1$ and $x[2n+1] = n$. You have $x[2n] = y[n]$ but $x$ is not periodic

Tryss
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