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adding triangle visualization for 1d
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contents/convolutions/1d/1d.md

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Note that in this case, the output array will be the size of `f[n]` and `g[n]` put together.
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Sometimes, though, we have an large size for `f[n]` and a small size for `g[n]`.
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In this case `g[n]` is often called a *filter*, and often times when we are using a filter on an array (that might represent an image or some form of data), we want the output array to be the same size as the input.
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The simplest interpretation for this is that at every point $$x$$ along signal one, the convolutional output will be composed of one part $$x-1$$, two parts $$x$$, and one part $$x+1$$.
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If we perform a convolution with signal one and this filter, we will find that the square wave is smeared a little at the edges, like so:
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ADD ANIMATION
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<div style="text-align:center">
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<video style="width:90%" controls loop>
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<source src="../res/1d_triangle_animation.mp4" type="video/mp4">
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Your browser does not support the video tag.
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</video>
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</div>
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This specific case is similar to a Gaussian, which is a common kernel used for blurring images in two-dimensions.
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For this reason, we will discuss common kernels found in the wild in the next section on [convolutions of images](../2d/2d.md).
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