A visual introduction to the Fourier Transform

The Fourier Transform is an incredibly useful mathematical function that can be used to show the different parts of a continuous signal. As you can see from the Wikipedia page, the formula and the mathematical explanation of the Fourier Transform can get quite complicated. But as with many complex mathematical subjects, the FT can also be explained visually. In the video above, 3blue1brown breaks down the Fourier Transform into a really intuitive visual system that’s surprisingly easy to follow if you’re not a science or math person. This would have been super helpful in my physics and math classes in college.

See also Better Explained’s interactive guide to the Fourier Transform, which describes the FT metaphorically like so:

What does the Fourier Transform do? Given a smoothie, it finds the recipe.
How? Run the smoothie through filters to extract each ingredient.
Why? Recipes are easier to analyze, compare, and modify than the smoothie itself.
How do we get the smoothie back? Blend the ingredients.

The guide includes interactive graphs that you can play around with. Stuff like this always gets me so fired up about math and science. Ah, the path not taken…

• mathematics
• science
• video