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I'm facing confusion about the definition of the convolution between two discrete periodic signals.

Basically, the definition of convolution between s and t is defined as :

enter image description here

In the operation, while the index of s is increasing ([0, K-1]), we have the index of t doing the opposite [n, n-K+1].

But here for example, the convolution is also employed, but the situation is different. And from my understanding, convolution in this case could be defined as :

enter image description here

And now we can see that the indices of s and t are moving in the same direction and the result will be totally different if we compare it, with the first definition.

At this point, I'm hesitating between convolution, circular/cyclic convolution, or even cross-correlation. As a bonus, I'd be grateful if you could also clarify the difference between these terms.

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    $\begingroup$ dsp.stackexchange.com/a/82410/50076 The "computational" perspective the answer describes, also reflects CC's motivation (but not conv's). The reading it links (old, should say CH6) explains CC well, if CC is treated as a time-reversed kernel (valid for real-valued only) $\endgroup$
    – OverLordGoldDragon
    Jun 28 at 12:11
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    $\begingroup$ Thanks, @OverLordGoldDragon. I'll go through it. $\endgroup$
    – Franck Might
    Jun 28 at 12:27

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