And can we understand this in sort of a pictorial way

rather than actually going through and doing the integrals at all these points?

Can we just look at our filter and look at our signal and

get some idea of what will be going on?

And the answer is yes, and the reason is that more or

less a filtering system or a linear system is looking for

parts of the inputs, parts of that resemble the filter.

So the more the input signal resembles the filter,

the higher your output signal will be.

So, if you look at our filter up here, you will see it doesn't,

none of the actual inputs stay too close to the filter, but

if we find the part of the input signal that looks the closest to the filter,

which would be the one where, the one over here around this zero crossing,

that is going to be the signal that yields the highest output.

Because it is a signal that,

it is the part of the signal that looks most similar to the filter.

Because that's the case, because our linear system is looking for

certain features of the input signal,

sometimes we call a linear system a feature detector and

this means that the liner systems responds most strongly

when it encounters a part of the input that looks like it's filter.

So the filter describes the feature that the system is looking for.

And in this week's lectures,

we talked about ways of trying to just start with the output and the input and

try to figure out what feature the system is looking for.

So we try to figure out what filter

the system is using to go from its input to its output.

And in neuroscience you can use methods like reverse correlation or

spike-triggered averaging.

Or spike-triggered covariance analysis to estimate what the filter looks like.

One last note that's not super important for our purposes, but if you go into

an engineering field after this or have come from an engineering field after this,

just be aware that sometimes, when you actually see the math written out,

they will draw the filters backwards.

Meaning that they're flipped around the y axis.

And this is just, kind of a convention people use that

makes writing out the integral a little bit easier.