February 2nd, 2004

Ooh, I was on a roll.

I understand convolution a bit better now and I just had an exam in that class too, which is nice. It seems that we must multiply every value together and sum them all up, so that we can let past and future values affect the current value. Say I've got a device that counts to ten; it will need to use past values to determine what the next number is. If it doesn't know that it already counted to four, then how can it count to five? So for each value, we must take all the old values and future values and multiply them by the values of our system impulse response to let us really fuck with a signal. I mean, without convolution, we'd still be adding five to our current value, or maybe multiplying it by seven. But now that we've got convolution, we can use all the values in our original signal to determine each and every output... together. It's like convolution lets the original signal be one big happy family and work together in a Dawson's Creek kinda way to create each individual output. So each output value comes from the combined effort of all the values in the original signal. Whew.

All this makes me think of how we covered memoryless systems so quickly. Memorylessness is related to causality in that causality says that we can only use old values and not future values, whereas memorylessness says that we can only use the current value, none of the past and present ones (So in effect, with memorylessness we're stuck with multiplying and adding to the current value like I said before). But despite the fact that we covered memorylessness so quickly, it seems to be the key to understanding why convolution is the way to screw with signals. Or rather, it's because of memoryfullness. Convolution allows for memoryful systems that allow past and future values to effect the current output.

To be fair though, I still don't see why we have to flip the signal before we do all this crap. I mean, now I've seen the light that is the memoryful operation known as convolution, but why does it got to be flipped? I can still do all that crazy shit with an unflipped signal, but it's wrong. And I don't know why that is. Back to the books I suppose.

Damn. And now we're moving on to differential equations and the Z-Transform (I've been meaning to rent Dogtown and Z-Boys for a while now). Fortunately, I don't think it's very easy to "move on" from convolution. It's the monkey on my back.

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