Having a decent intuitive notion of Fourier transforms is an incredibly useful tool in your toolbox, even if you can't derive a Fourier transform by hand or write a fast Fourier transform (FFT) algorithm.
The basic idea is this: (almost) any (useful) signal can be represented as a sum of sine waves with different frequencies and phases. For example, an electrical signal or a sound wave is a one-dimensional signal where the x-axis is time. This might look like a really complex squiggly line that's hard to work with. Using a Fourier transform, you can separate the individual frequencies of that time-based signal. Then, you can modify the specific frequencies however you want. For example, if you have a lot of random, spiky noise in the signal, that will show up as high frequencies. To clean it up, just do a Fourier transform, throw out any data with a frequency above a certain threshold, and then run an inverse Fourier transform on the remaining data to get back a smoother version of the original signal. This is called a low-pass filter, and it's more or less equivalent to taking a moving average of the original signal.
Where it gets really fun is that you can extend this, in a pretty straightforward way, to higher dimensions. A two-dimensional signal, where both the x- and y-axes are space, is just an image. JPEG compression is based on this concept: it removes the high-frequency signal in the image in order to store the data in a more compact form, at the expense of losing some fine detail (or creating those ring-like artifacts, if you throw out too much data). Add a third dimension for time, and now you have video. And so on.
The nice thing about all this is that it's very visual, so you can get a good intuition for it without having to know all the math inside and out. Here's a good page with lots of visualizations and interactive examples: https://www.jezzamon.com/fourier/index.html
The basic idea is this: (almost) any (useful) signal can be represented as a sum of sine waves with different frequencies and phases. For example, an electrical signal or a sound wave is a one-dimensional signal where the x-axis is time. This might look like a really complex squiggly line that's hard to work with. Using a Fourier transform, you can separate the individual frequencies of that time-based signal. Then, you can modify the specific frequencies however you want. For example, if you have a lot of random, spiky noise in the signal, that will show up as high frequencies. To clean it up, just do a Fourier transform, throw out any data with a frequency above a certain threshold, and then run an inverse Fourier transform on the remaining data to get back a smoother version of the original signal. This is called a low-pass filter, and it's more or less equivalent to taking a moving average of the original signal.
Where it gets really fun is that you can extend this, in a pretty straightforward way, to higher dimensions. A two-dimensional signal, where both the x- and y-axes are space, is just an image. JPEG compression is based on this concept: it removes the high-frequency signal in the image in order to store the data in a more compact form, at the expense of losing some fine detail (or creating those ring-like artifacts, if you throw out too much data). Add a third dimension for time, and now you have video. And so on.
The nice thing about all this is that it's very visual, so you can get a good intuition for it without having to know all the math inside and out. Here's a good page with lots of visualizations and interactive examples: https://www.jezzamon.com/fourier/index.html
And this 3Blue1Brown video does a good job of explaining it: https://youtu.be/spUNpyF58BY?si=dz0z-s8NftW3Htun