0

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.

Franck Might
  • 53
  • 6
  • 1
    https://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) – OverLordGoldDragon Jun 28 '23 at 12:11
  • 1
    Thanks, @OverLordGoldDragon. I'll go through it. – Franck Might Jun 28 '23 at 12:27

0 Answers0