What is the Fourier Transform used for?

Gives an intuitive explanation of the Fourier Transform and discusses 6 examples of its use in every day applications.
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For a full categorised list of Videos and Summary Sheets, goto: www.iaincollings.com
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[@imarshad]

Such content should be definitely the introduction part of Fourier Transform mathematical course. This will definitely increase the level of participation and understanding of students knowing that they are starting to study something that has much more practical implementation and not just some boring theoretical thing.

[@iain_explains]

Yes, I totally agree. I'm glad you liked the video.

[@tomasscaballero4965]

​@@iain_explains just to reiterate what @imarshad has said, I am currently studying this subject and I cant thank you enough for providing some much needed context on its application. The content is brilliant! Thank you!

[@ger15100]

The Fourier Transform is also important in crystal structure solution, where one tries to obtain the atomic positions from a set of diffraction patterns. This is not necessarily a part of everyone's typical day, but it is for crystallographer's. And is also quite important since many modern inventions rely on knowing the internal symmetries of the crystals comprising them (pharmaceutics, energy, electronics). The Fourier Transform really is one of the greatest and widely used tools.

[@iain_explains]

That's very interesting. Thanks for sharing. I've had experience in signal processing for radar and medical imaging applications, both of which formulate problems of a similar form to diffraction patterns that you mention, so it's interesting to hear of the crystal structure application too.

[@ger15100]

@@iain_explains I have read some articles about signal to noise ratios in medical imaging. I was trying to find a suitable metric for my work. It might be worth it for me to check out some papers on those topics in more detail, then. They might offer insights into problems faced by crystallographers today. Thanks for the suggestion.

[@simirose5507]

I wish, I had a professor like you in my studies Keep up the good work Sir! Thank you

[@iain_explains]

Thanks for your nice comment. I'm glad you liked the video.

[@dhirendusomani]

Best Video I've came across on Fourier Transform and it's real life application.

[@iain_explains]

I'm glad you found it helpful.

[@fredericorod]

Thank you. Your videos are helping me a lot. I gave me a break of telecommunication engineering course last year, and now I’m back, I’m trying to get all definitions and understandings back again. You teach in a so easy way, it’s amazing.

[@iain_explains]

That's great to hear. I'm glad you're finding the videos helpful.

[@se2702]

I love how you've explained things in a practical manner. This helps in the understanding of Fourier Transform by examples. Thanks Iain!

[@iain_explains]

Glad it was helpful!

[@alexmxy2231]

Please do more of these videos!!! Love to see more of these real life applications and examples

[@iain_explains]

I'm glad you like them. I've got a couple more in mind, but they do take a bit more time to make. Hopefully I can get them done soon.

[@eminbilir1448]

I am following all of your videos in your channel and absolutely its really impossible to desribe how beneficial they are , really appriciate your effort thank you so much :)

[@iain_explains]

It's my pleasure. Thanks for your nice comment. I'm glad the videos are helpful.

[@alpargur]

Sir it's a nice video. These topics sometimes get too abstract to comprehend and it's very valuable to give some concrete real-world examples. Highly appreciated!

[@iain_explains]

That's great to hear. I'm glad you found it useful.

[@ANJA-mj1to]

The mystical meaning of Fourier transform full of the measurements and proportions someone unknown and as a mare tool of the engineer like me - this is monolithic topic. Impressive how revolutionary the actual Fourier transform You present - this is the complete and rigorous proof of Fourier transform in natural world. I can see the physical variables of time and frequency like one formal Fourier statement of a Fourier transform, i. c. I ADMIRE YOU FOR YOUR WORK WITH SUCH EMPHASIS AND ALL THE KNOWLEDGE ESSENCE YOU STRUCTURE YOU BRING TO LIGHT FOR US! Thank you prof. Iain!

[@iain_explains]

That's great to hear. I'm so glad you like the videos.

[@edmundkemper1625]

Nice explanation Professor! Your effort to explain Signal Processing Practically is very much appealing.!

[@iain_explains]

Glad you liked it

[@HaSongSon123]

OMG. I love you so much, Prof. Iain. Keep going please! I always look forward to your new videos.

[@iain_explains]

Thanks for your nice comment. I'm glad you like the videos.

[@prithvisangani]

Outstanding. Had a clear learning experience

[@iain_explains]

Glad it helped

[@viahttp]

Thank You so much for your explaination. This is what students should know before even they start learning. Because lot of them has not idea why even they are learning what they are learning. Many Thanks for your explaination.

[@iain_explains]

Thanks so much for your nice comment. I'm glad you liked the video. I try to make the kind of videos that I would have liked to have seen when I was a student. So I'm very glad that others are finding them useful too.

[@speedbird7587]

Thank you You really brought me deep into very nice applications of fourier transform

[@iain_explains]

I'm so glad you found the video helpful.

[@mohamedtarek-lz8bu]

perfect video and perfect examples !

[@iain_explains]

Glad you liked it!

[@mrfares7271]

Thank you for this wonderful tour

[@iain_explains]

Glad you enjoyed it

[@claestom1]

Thanks a lot for this explanation sir!

[@iain_explains]

Glad you liked it.

[@emadibnalyaman8073]

Thank you very much, your making Telecommunication easy to understand.

[@iain_explains]

I'm really glad you're liking the videos. That's great to hear.

[@Mark-ju7pe]

amazing content Ian!

[@iain_explains]

Thanks. Glad you enjoyed it.

[@joshallentabiosas4809]

thank you, this helps us alot

[@iain_explains]

Glad to hear that!

[@beatalert123]

Awesome video. Thanks ian 🎉🎉

[@iain_explains]

Glad you liked it.

[@user-wr5jq3sj6j]

Thank u for this superb video!

[@iain_explains]

I'm glad it was helpful.

[@bpfurtado]

Awesome content.

[@iain_explains]

Glad you liked it

[@andrespasca4329]

Amazing video! 👌

[@iain_explains]

Thanks! 😀

[@kushalnanote4800]

Very nice Explaination of such confusing topics ,videos very helpful for my studies.🙏

[@iain_explains]

Glad to hear that

[@hashirkhattak9180]

you are an inspiration sir

[@iain_explains]

I'm glad you liked the video.

[@davebordenkircher8131]

Could you make a video on spatial correlation in wireless MIMO systems?

[@iain_explains]

Have you seen this video from the channel? "Statistical Modelling of MIMO Communication Channels" kzbin.info/www/bejne/h2Sbk3uorsyDkMk

[@sathyanarayanankulasekaran5928]

big fan of this explanation

[@iain_explains]

That's great to hear. I'm glad you like the video.

[@emanueleziglioli499]

Now, this example reminds me of the Audiomoth device. It's really cheap and quite wideband. It allows you to record bats way beyond the human acoustic range.

[@iain_explains]

Interesting. I hadn't heard of that device.

[@emanueleziglioli499]

@@iain_explains useful now also as a USB microphone, forgot to mention

[@jamesjohn2537]

Thanks a lot

[@iain_explains]

Most welcome

[@arjunsnair2203]

Thank you sir

[@iain_explains]

My pleasure.

[@user-jc3yo3on2b]

Thank you so much ❤

[@iain_explains]

You're welcome 😊

[@muhammadelbecy627]

thank you prof

[@iain_explains]

You are welcome

[@emanueleziglioli499]

A topic I've been wondering for some time now is why in RF we capture and transform complex numbers, while acoustic applications are perfectly happy with real numbers. One explanation I have is that for acoustic, real time applications it's critical to add little or no delay, so often IIR filters are used, that add phase distortions. But apparently our ear is not so sensitive to phase (I guess, high frequency, but middle to low frequency phase distortions would mess with perceived direction of arrival). And what about image transforms, that again use DCTs?

[@iain_explains]

Hopefully this video will help: "What is a Baseband Equivalent Signal in Communications?" kzbin.info/www/bejne/m6W9coWXgrOBaNU

[@emanueleziglioli499]

@@iain_explains ok, I'll see you there

[@emanueleziglioli499]

@@iain_explains hi Iain, I saw that video but I'm not convinced. Ok, audio signals are low in frequency so we don't need to demodulate them from IF. But still, if we used an acoustic signal to transmit a QAM modulation we would need to perform complex sampling (or deriving IQ with a Hilbert transform). I guess the fundamental reason why acoustic signals are only sampled real is simply because they're not typically digital communication systems.

[@iain_explains]

​@@emanueleziglioli499 Well, not really. It's actually because we are only interested in a small bandwidth around the central "carrier" frequency when we're considering RF (or any "bandpass" signal). It's not specific to digital communication systems. What's important is that we sample (or "capture", as you put it) sufficient statistics to be able to fully define the continuous time signal. If it is a lowpass (or baseband) signal, then we can do this by sampling real-valued samples at a sample rate that is twice the highest frequency component of the signal. If we have a bandpass signal, then we're not interested in any of the frequencies in between the zero frequency and the lower frequency in the "passband" of interest. And so, instead of sampling at more than twice the RF/carrier frequency (which would require extremely fast ADCs), instead we "down convert" to a lower frequency and then sample that signal. The thing is, when we "down convert", we do this with a sinusoidal signal. Now, any sinusoidal signal will have another orthogonal sinusoidal signal at the same frequency (90 degrees out of phase), and since they are orthogonal, you need to down convert with that one too, so that you don't miss any important information of the RF signal. So now you have two "down converted" signals, which both need to be sampled. We represent these two signals with "complex valued" samples. One sample from each of the two orthogonal down-converted signals. Hope this explains it.

[@iain_explains]

Hi Emanuele, I've just made a video to explain this. You might like to check it out: "Sampling Bandlimited Signals: Why are the Samples "Complex"?" kzbin.info/www/bejne/gJjPg3qInt-kfa8

[@I0MSammy]

This is so awesome Iain! I am in Signals and Systems this semster and studying filter design in another course. This video is very motivating!

[@iain_explains]

That's great to hear. I'm glad it was helpful!

[@mohamadfawaz4146]

perfect!

[@iain_explains]

Thanks. I'm glad you liked it.

[@daydreamer05]

Students are lucky in your offline classroom. Wish I'd one of them.

[@iain_explains]

Glad you like the videos.

[@omsingharjit]

i am interested in Ft or FfT because it's used in Spectrum analyser but wondering why it's FfT which is used instead of ft and what is the difference between ft and FfT !

[@iain_explains]

This video will help: "How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?" kzbin.info/www/bejne/aJywhH-ndsd_oJY

[@omsingharjit]

@@iain_explains i have watched this video but after watching some video i found that FfT is just fast efficient FT algorithm that you only mentioned briefly so the difference is clear to me .

[@iain_explains]

Actually, it is a fast efficient implementation for performing a Discrete Fourier Transform (DFT) (which is not exactly the same as the Fourier transform which is in continuous time).

[@galabhjoshi8842]

Is it me Or anyone else also find this man like Heisenberg of Breaking Bad? Btw loved the video...... Never seen such a practical explanation 🔥🔥🔥

[@iain_explains]

😁😎 Glad you liked the video.

[@helloworld-fv8kx]

good bike! i like it ❤‍🔥

[@iain_explains]

Thanks 🔥

[@gator1984atcomcast]

Still don’t understand. Seems like filtering could be done with electric circuits on analog signals. Evidently a computer can operate on digital signals much the same way. Show me!

[@iain_explains]

Feel free to check out my videos at iaincollings.com where there is a full categorised listing of topics, including discrete time (digital) signals. If you're interested in how the continuous-time Fourier transforms relates to the discrete-time Fourier transform, then check out: "How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?" kzbin.info/www/bejne/aJywhH-ndsd_oJY and "How does the Discrete Fourier Transform DFT relate to Real Frequencies?" kzbin.info/www/bejne/pnqpq2tqpM9smaM ... and next time, you might like to be a little less "demanding" in your comment. I seriously considered blocking your comment, but have decided to reply. I'm not in the habit of responding to demands. A little politeness will go a long way.

[@om25396]

Wow😮😮

[@iain_explains]

I'm glad you liked the video.

[@austinbristow5716]

Why is the information you get in the frequency domain more useful than the information you get in the time domain? (For the purposes of signal processing)

[@austinbristow5716]

More specifically, could you either comment or make a video on what kind of useful information can you (in general) extract from the time domain, and what useful information can you extract from the frequency domain. Maybe specific examples which demonstrate the utility of the frequency domain vs the utility of the time domain? What information about the signal do you gain/lose when in the time vs frequency domain? Thank you !

[@iain_explains]

Good question. First I should make the point that the same "information" is contained in both the time-domain representation, and the frequency-domain representation. No "information" is lost when transforming from one domain to the other. However, viewing that information in different ways, can certainly reveal different things to you. If you'd like some examples of the uses of the frequency domain, you might like to watch this video: "What is the Fourier Transform used for?" kzbin.info/www/bejne/jKXFg5iietOgqZo

[@pitmaler4439]

The picture with the FT from the frog and the bird: it is only an example, that's clear. From whole FT (picture left) you cannot get the FT of different animals, can you? You only know that both are inside, not more, I assume.

[@iain_explains]

It's basically a "pattern matching" problem in the frequency domain. The frequency characteristics of a frog (ie. the "shape" of the function in the frequency domain), are different from the frequency characteristics of a bird. If your measured signal has sounds from both a frog and a bird in it, then the frequency domain will contain both "frequency characteristics" added together, and it is a question as to whether your signal processing "matching" software can pick them both out.

[@seshansesha7645]

Thanks for your Pragmatic approach to explain the real usage of these wonderful mathematics...thanks to "Jean-Baptiste Joseph Fourier"

[@iain_explains]

Glad it was helpful!

[@IVBURAK]

canım benim

[@omsingharjit]

i only likes maths if it is explained by its application