I'm very new to DSP, and I'm unsure about finding how a signal $y[n]$ would look like. The following is given:
Assume we have a finite support signal $x[n]$ which has the values $1, 2, 3$ for $n = 1, 2, 3$ and $0$ otherwise.
Now we have the periodic repetition of this signal, call it $y[n] = \sum_{k=-\infty}^\infty x[n+5k]$.
To understand how the periodic signal would look like, I'd like to write down a few samples and plot them.
First, I wrote down the values of $x[n]$ like so:
n | x[n] |
---|---|
... | ... |
0 | 0 |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 0 |
... | ... |
Now for $y[n]$, I tried the same:
n | y[n] |
---|---|
... | ... |
0 | $\sum_{k=-\infty}^\infty x[0+5k] = 0$ |
1 | $\sum_{k=-\infty}^\infty x[1+5k] = 1$ |
2 | $\sum_{k=-\infty}^\infty x[2+5k] = 2$ |
3 | $\sum_{k=-\infty}^\infty x[3+5k] = 3$ |
4 | $\sum_{k=-\infty}^\infty x[4+5k] = 0$ |
5 | $\sum_{k=-\infty}^\infty x[5+5k] = 0$ |
6 | $\sum_{k=-\infty}^\infty x[6+5k] = 1$ |
7 | $\sum_{k=-\infty}^\infty x[7+5k] = 2$ |
8 | $\sum_{k=-\infty}^\infty x[8+5k] = 3$ |
9 | $\sum_{k=-\infty}^\infty x[9+5k] = 0$ |
... | ... |
Would the above list of samples for $y[n]$ be correct?