What is the Fourier Transform used for? 

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

​@@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!

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.

@@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.

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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.

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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.

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Interesting. I hadn't heard of that device.

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

Thanks 🔥

Have you seen this video from the channel? "Statistical Modelling of MIMO Communication Channels" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Q38bHrygPZg.html

This video will help: "How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2kMSLqAbLj4.html

@@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 .

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).

Hopefully this video will help: "What is a Baseband Equivalent Signal in Communications?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-etZARaMNN2s.html

@@iain_explains ok, I'll see you there

@@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.

​@@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.

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"?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-JglRGRizqGM.html

I'm glad you liked the video.

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?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2kMSLqAbLj4.html and "How does the Discrete Fourier Transform DFT relate to Real Frequencies?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pIFz84oj9cA.html ... 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.

Glad it was helpful!

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 !

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?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-VtbRelEnms8.html

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.