adding a few more changes to convolution chapter(s)

Author: leios

contents/convolutions/1d/1d.md

@@ -16,7 +16,13 @@ This means we basically just need to keep one array steady, flip the second arra
 
 This can be seen in the following animation:
 
-ADD ANIMATION
+<div style="text-align:center">
+<video style="width:90%" controls loop>
+  <source src="../res/1d_gaussian_animation.mp4" type="video/mp4">
+Your browser does not support the video tag.
+</video>
+</div>
+
 
 Note that in this case, the output array will be the size of `f[n]` and `g[n]` put together.
 Sometimes, though, we have an large size for `f[n]` and a small size for `g[n]`.

contents/convolutions/convolutional_theorem/convolutional_theorem.md

@@ -20,7 +20,7 @@ This is because of something known as the *convolution theorem* which looks some
 $$\mathcal{F}(f*g) = \mathcal{F}(f) \cdot \mathcal{F}(g)$$
 
 Where $$\mathcal{F}$$ denotes the Fourier Transform.
-Now, by using a Fast Fourier Transform (fft) in code, this can take a standard convolution on two arrays of length $$n$$, which is an $$\mathcal{O}(n^2)$$ process, to $$\mathcal{O}(n\log(n))$$.
+Now, by using a Fast Fourier Transform (FFT) in code, this can take a standard convolution on two arrays of length $$n$$, which is an $$\mathcal{O}(n^2)$$ process, to $$\mathcal{O}(n\log(n))$$.
 This means that the convolution theorem is fundamental to creating fast convolutional methods for large inputs, assuming that both of the input signals are similar sizes.
 That said, it is debatable whether the convolution theorem will be faster when the filter size is small.
 Also: depending on the language used, we might need to read in a separate library for FFT's.