The Fourier Series and Fourier Transform Demystified

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Creator - Jade Tan-Holmes
Script - Simon Morrow, Simon Mackenzie, Dean Berwick and Jade Tan-Holmes
Music - epidemic sound

[tone]

That explanation of the Fourier Transform is probably the most intuitive I've ever heard!

[earthling_parth]

Finally!!! This was my Eureka moment. I've studied Fourier Series and Transformation multiple times during my bachelor's and masters in computer science and each time I only learned the technique and not _why_ and _how_ it's used. This is the best explanation and intuitive explanation of Fourier Series and Transformation I've ever encountered. Thank you so much Jade! You must've researched really hard to come up with the examples and simpler words to explain this. Thank you once again ♥️

[ohnonomorenames]

When ever I watch one of Jade's videos i feel like I am watching and adult version of Playschool (an Australian kids educational TV show) there is a level of enthusiasm and 'you can do this' that comes through that is so wonderful. I often get lulled into a false sense of security and zone out and then have to go back and re-watch remembering that I'm not quite as smart as she makes me feel. Jade I love everything about the way that you do what you do it must take a mountain of work so thank you so much.

[burningsilicon]

One thing to note is the (w) omega in the fourier transform is a continuous variable.The visual showed only integer frequency’s sin(1x), sin(2x)…sin(nx), but (w) can be any real number like 2.5, pi/4, etc.

[lvmbk]

Being a telecommunication engineer I perfectly know how Fourier transforms are ubiquitous, as they are necessary for signal processing an electronic communications. But it is fundamental also for buildings and mechanics because the analysis in the frequency domain allows to understand how materials and systems behave under given inputs.
I think nowadays it is as essential as basic math operators like +, -, /, *, etc....

[Dixavd]

You've become such an amazing educational video creator, Jade! The cinematography amazing: lighting, camera quality, colour-correction, framing, pacing, , etc... You've even mastered how to use these skills to effectively get your point across without it becoming a distraction.
I supported you on patreon previously but had to stop for financial reasons and I then didn't keep up with your uploads (mostly because my physics studies became so exhausting, I rarely had the energy to watch physics videos for fun). I'm so glad I looked you up again, though. I'm very proud of how far you've come. Keep it up.

[SKULDROPR]

This concept blew my mind the first time I learned about it at uni. Until then, I had never realised, or even considered you could transform from one domain to another. I'm now an audio engineer, it's astonishing how ubiquitous, useful and practical the Fourier transform is in the field. I liked the tie in to real world algorithms at the end. I would like to see a video about different sorting algorithms if possible! My personal favourite is the radix sort.

[trewaldo]

This is my most favorite topic in introductory signal processing where signals in the time domain exhibit a certain characteristic in the frequency domain through respective spectral properties. Thanks, Jade, for the animated and colorful video! Cheers! 😍🤓🥰

[rohank]

so may years spent trying to understand fourier series and transform and then this one 14 minute long video comes along and makes things all so clear. Thank you

[HALK]

This is in my math curriculum and i was soo obsessed by them, thanks for this video

[divitrajgogia]

The best video on YouTube for Fourier transform and analysis! Please make more videos on this part of physics/ engineering. This feeling of understanding and visualization of Fourier transforms is extremely satisfying! Thanks for making a great video.

[GarryMah]

Fourier transform was a topic I could never understood during my undergraduate studies almost 2 decades ago. I'd always skipped any Math examination question that require us to use Fourier transform.
While I still doubt I'll ever be able to comprehend the mathematical part of it, your video actually gave me a great idea of what Fourier series and Fourier transform is all about. Thank you.
I wished we had resources like this 20 years ago, lol. It helps make sense of all the abstract mathematical concepts we had to learn.

[adsbhushan]

Thanks for cracking open a black box, I've been carrying since college physics. Brilliant exposition and the accompanying video makes it easier to understand.

[ehrichweiss]

I've always love the Fourier transform. I first learned of it back in the early 1990s when I was using a "granular synthesizer" that would let you draw a picture and then it'd convert that into sound. It took over 20 years for some software to duplicate that synthesizer. BTW, my wife and I bought your t-shirts and we love them. Keep up the good work.

[BleuSquid]

My favourite usage, and indeed my introduction to, the Fourier Transform is in Mersenne primality testing. The most computationally expensive part of some primality tests is a squaring of a very large integer. By representing the digits of the number as time-series array, taking the fourier transform, squaring the individual elements (this step can be done massively parallel, hello GPU computing!), and then transforming it back, we have effectively squared the original number in a fraction of the time.

[mitchwyatt]

Around the 12 min mark, The orthogonality was glossed over a bit here, but it's an important point - the orthogonality is what keeps the calculations for decomposition into component sin and cos waves (relatively) simple.

P.S. Fantastic video overall. I really think this is my favorite yet of all your videos. Please keep up the good work!

[loberd]

Thanks for the video. I’ve been a chemist in industry for 15 years. I learned it back in college but wasn’t great with it. I’ve had to “black box” it (use without a firm understanding) in explanations for instrumentation I use (FT-IR) and some instrument designs I’ve worked on. This is a great explanation. Not sure it’s a refresher for me as I wasn’t solid on it when I learned it.

[yasscat]

1:04 you mean a higher frequency* great explanation exactly when I needed it <3

[shunpinhsu]

Fourier series works mainly on `periodic' functions. Aperiodic functions are treated as periodic functions with their periods tending to infinity. In this case, the Fourier series (in the form of summation) takes the form of integration, which is known as the Foruier transform.

[fiNitEarth]

This video is FANTASTIC!
I've been using the Fourier transform in data science a lot and thought I had a pretty good understanding of the matter. This video however gave me a whole new intuition for it.
By far the best video on Fourier I've ever seen!!