Okay. This is decent. I do like the idea of "fancy multiplications" because I do think you should understand convolution as well as you understand multiplication.
But I still feel like this kinda obscures and confuses the origin of the reversal.*
If you don't understand the convolution formula instinctively, read this comment enough times till you do.
The point is this.
-We have a function originBangSound(t) that maps the effect at (t) of an impulse or "bang" coming from the origin (t=0).
-We have a function bangWeights(t), which measures the distribution of impulses or "bangs" over time.
-The question is: how do we get the total allBangSounds(t)?
Simple: We make every point in time the origin, and add all the results together. Let's call (tau) the current origin. The size of the bang at this origin is bangWeights(tau). The size of the sound at (t) which is coming from this origin is originBangSound(t- tau), since we care about the position of (t) relative to the current origin (tau). Adding them up leads to an integral in the continuous case.
The point is this. Don't think of it as a flip. Think of (tau) as defining the origin point for a particular "bang".
Here's a nice sanity check: if (tau) is larger than (t), (or equivalently, (t-tau)<0) then do you expect to hear its bang? Ofcourse not. The bang hasn't happened yet. So unless its bang travels backward in time (which definitely does happen in spatial convolutions!) you ain't hearing it.
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*Come to think of it, this is a very useful pun. When you think to yourself "what's the origin of the reversal again?", just remember, the moving the origin is the origin of the reversal.
But I still feel like this kinda obscures and confuses the origin of the reversal.*
If you don't understand the convolution formula instinctively, read this comment enough times till you do.
The point is this.
-We have a function originBangSound(t) that maps the effect at (t) of an impulse or "bang" coming from the origin (t=0).
-We have a function bangWeights(t), which measures the distribution of impulses or "bangs" over time.
-The question is: how do we get the total allBangSounds(t)?
Simple: We make every point in time the origin, and add all the results together. Let's call (tau) the current origin. The size of the bang at this origin is bangWeights(tau). The size of the sound at (t) which is coming from this origin is originBangSound(t- tau), since we care about the position of (t) relative to the current origin (tau). Adding them up leads to an integral in the continuous case.
The point is this. Don't think of it as a flip. Think of (tau) as defining the origin point for a particular "bang".Here's a nice sanity check: if (tau) is larger than (t), (or equivalently, (t-tau)<0) then do you expect to hear its bang? Ofcourse not. The bang hasn't happened yet. So unless its bang travels backward in time (which definitely does happen in spatial convolutions!) you ain't hearing it.
_____________________________
*Come to think of it, this is a very useful pun. When you think to yourself "what's the origin of the reversal again?", just remember, the moving the origin is the origin of the reversal.