This will be my 12. post but I have deleted all the previous ones because I believe that this outline is so much better. HELLO AGAIN, WELCOME TO MY BLOG.
In this post, I will be explaining a topic I discovered and plan to investigate further: Fourier Transforms
What are fourıer transformS
They are one of the most puzzling math concepts I have ever come across. They are the building block of many engineering-based applications, music, image recognition and many more.
How does a fourıer transform work
Such a great question(actually a pretty intuitive one lol). Before diving deep into Fourier transformations, I want you to think of a wave of a string of guitar. It’s frequency-time graph is plotted. (image1)
Just a simple sinusoidal wave, right? Except it is shifted upwards because we can’t have negative frequencies. Now, imagine when the equation when a guitarist hits two string for a chord, or even three in many cases. There will be multiple sinusoidal functions with different amplitudes and frequencies. The frequency time graph will therefore become the sum of amplitudes of multiple functions alternating with different frequencies. When we plot the entire function, it will rather be an uglier function.(image2)
Let’s assume that there is a point in the recording where the high frequency worsens the track and I, the guitarist want to remove that frequency. What should I do? I can’t reach any conclusions from the graph above because it is made up from multiple sinusoidal graphs, leaving me unable to interpret. So I ,being the jacked smart scientist I am, find a way to break down the function to its component sinusoidal functions. How: Fourier Transformations
In this post, I wanted to present an example of how we use Fourier transformations to analyze complex structures, using an analogy from the guitar. In the following posts, I will be continuing explaining Fourier series a bit mathematically and practically as well. I plan to make 4 total posts about Fourier series theory. Then, I have some ideas that you will see :). See you guys on the next post!
- This one
- The “almost Fourier transform”
- The Fourier transform
- It’s applications
caganTECH 
Leave a comment