What is the Fourier Transform? ("Brilliant explanation!")
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- Опубліковано 7 лют 2025
- Gives an intuitive explanation of the Fourier Transform, and explains the importance of phase, as well as the concept of negative frequency.
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Related videos: (see www.iaincolling...)
• What is the Fourier Transform used for? • What is the Fourier Tr...
• Visualising the Fourier Transform • Visualising the Fourie...
• Fourier Transform Equation Explained • Fourier Transform Equa...
• Is Phase important in the Fourier Transform? • Is Phase important in ...
• What is Negative Frequency?: • What is Negative Frequ...
• How do Complex Numbers relate to Real Signals? • How do Complex Numbers...
• Delta Function Explained: • Delta Function Explained
• Sampling: • Sampling Signals
• Fourier Transform of Cosine Function: • Fourier Transform of Cos
• Fourier Transform of Cosine with Phase Shift: • Fourier Transform of C...
• How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related? • How are the Fourier Se...
• Typical Exam Question on Fourier Transform Properties • Typical Exam Question ...
For a full list of Videos and accompanying Summary Sheets, see the associated website: www.iaincolling...
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I really dig this format. Pen, paper, great explanation - nothing else required.
Glad you like it!
Dear sir, Can you please make a video series on x ray diffraction.
I'm an industrial and telecom engineer who liked those signals and systems concepts a lot when I studied them, and I'm so impressed by how well you make perfect videos on virtually all of them. You have my full recognition, 10/10 as a professor, no doubt this is already the overall opinion of your lucky students.
Thanks very much for your nice comment.
Brilliant explanation!
At the university we just get bombarded with the formulas without a clear intuition of what’s really happening when we apply them.
A well deserved subscription 👍👍
Glad it was helpful!
Bosss you really understand everything once you seen this video.
The way you explain things is unbeleivable Iain. From reading several communication articles with many terms I do not understand, I now have a treasure of wonderful lectures that perfectly explain ALL of the things I need to know. You are one of a kind Iain !!!
That's so great to hear. I'm really glad you're finding the videos useful.
Never knew that there exist a professor that explains FT so well.....thank you sir
Glad you found it helpful.
Sir, I am writing this comment from Turkey. I really appreciate your insightful explanations. You really helped me to understand. I learned somethings from University but I didn't know what exactly I know, what all of the things are. Thank you very much professor.
I'm glad to hear you like the videos. Have you discovered my website that has a full categorised listing of all the videos? iaincollings.com
@@iain_explains oh I didn’t know the website. Thank you very much. I don’t know why everybody is teaching this lecture in hard ways. I really was looking to explanation videos and I found a huge EXPLANATION CHANNEL😁 so thank you professor, you really helping to the students🙏🏼
I’ve worked in industry for 35 years now. I discovered your videos recently, and they are extremely clear, insightful, and enjoyable. I haven’t been excited about anything on UA-cam until now. Thank you. I do have a bit of an off topic question: what do you use for your camera and overhead view? I would like to use a similar set up for design reviews (more technical interaction and less slides).
Thanks for your nice comment. I'm glad you like the videos. If you drop me an email, I'll send you a photo of my setup. (I'm sure you can search and find my university email easily).
Simple and to the point explanation. Though i am no longer a student but still i love watching mathematics videos and you are a very good teacher.
Thanks very much. I'm glad you like the videos.
Thanks a lot Ian, I got this in class many years and now I'd like to use it again this a great refresh. So is the rest of your channel, thanks for the taking the time!
Glad it's helpful!
Wow. This video is amazingly intuitive and makes the concept of the Fourier transform easier. Thank you for the fantastic contents!
Glad it was helpful!
You are such an awesome Professor - so glad angels like you take the time to help struggling students out.
Definitely won‘t be the last video I watched, will recommend you to my colleagues
Cheers from Austria (no kangaroos)
Thanks for your comment and support for the channel. I'm glad you're finding the videos helpful.
Thank you very much professor. You explain everything in such a simple way. Can't be grateful enough. Greetings from Greece!
Thanks for your nice comment. I'm so glad you like the videos!
Thank you so much it helps a lot to understand the representation of sinus because of the minus that's contain. It was brief and clear thank you another time, wish you a better continuation ❤️
Glad it was helpful!
You are a very good teacher. Love the way you explain things in a very clear and concise manner.
Thanks. I'm glad you like the video. Have you seen my webpage with a categorised listing of all the videos on the channel? iaincollings.com
@@iain_explains i have checked that out and all of the lectures are awesome! Only regret is that I wish I could have found your lecture when I was an engineering student 😂🥹.
Wow this was amazing! I've got Fourier Transform in a university class and was a bit lost. But this video was so good!
THANK YOU!!!
Great. I'm so glad it helped!
These videos shows the deep command over the subject by the humble instructor. Thank 🙏 You so Much!!
You're very welcome!
Wow very neat and clear explanation. I'm a physics student. I'm having dificulty in understanding Fourier transform in quantum mechanics and wave optics. You explained it very easily.Thank you so much.
You are most welcome
Thank you professor 😇😇😊😊
My sem exams are near ..these videos are really helpful
I'm glad you like the videos. All the best for your exams.
One thing to note is the reason for storing both sine and cosine amplitudes for each frequency. A sine and cosine function at the same frequency, when summed together, can represent all possible phases of the incoming signal solely through changing their amplitudes.
Thank you very much Iain I highly appreciated I got lost with my FT your video helped me to find my way, I'm very thankful to you
Glad it helped
I felt like a solution for a mystery....wow thats great explanation 😮 for fourier transform....
I can bet even now my college professor doesn't know or how to explain the fourier transform...
Watching this video from Tamilnadu, India 🇮🇳
❤
I'm so glad you liked the video.
Really loving these videos !!
Glad you like them!
I can't thank you enough for this video. Thanks for the very clear and easy-to-understand explanation.
Glad it was helpful!
Many thanks for such great videos and clear explanations!!!.
Glad you're finding the videos helpful!
Remember watching this when i was 16, came back at 18 and instantly understood it.
Nice one! 😁
Thank you, simple and easy to understand.
Glad it was helpful!
a simple and intuitive interpretation. thanks a lot
Glad you liked it!
Thank you Sir,you are a life saver!
Glad you found the video helpful.
I salute you prof. from lebanon - beirut...great educational lectures
I'm glad you like them. It's great to be able to help people all over the world.
I'm gonna tell all my EE friends about this channel now that I discovered it, you are a lot better at explaining things than my professors 😆
Glad you're finding the videos helpful.
Amazing explanation, clear and simple, many thanks
Glad it was helpful!
Thank you prof. You really shed light on complex concepts that are difficult to understand without teacher. In Farsi, "damet garm".
Glad you found the video helpful.
You are really WAY better than my professor.... You saved my life. I will come back with an A+ !!
Thanks for your nice comment. Glad I could help!
Thanks for sharing such informative video this help me to understand forier transform ,,,,,,,,
Great. Glad to hear.
thank you sir for your great explanation
You are most welcome
You're amazing, thank you so much
You're so welcome!
Thank you for the great video! Could you please explain the phase part a bit more? I can't quite understand how you get the -pi/2 and pi/2 phases.
Hopefully these videos will help: "Fourier Transform of Cos with Phase Shift" ua-cam.com/video/97eKhJwf9Mk/v-deo.html and "Is Phase important in the Fourier Transform?" ua-cam.com/video/WyFO6yBQ0Cg/v-deo.html
@@iain_explains Thank you very much!
this is really awesome...thanks for the beautiful explanation...just one request just disable the autofocus and manually set the focus on the paper...the focus will not jump around.
Yes, thanks for the suggestion. I've tried looking in the past for ways to do it, but couldn't find how. I just use a phone for the camera and there are lots of posts saying it's not possible. However ... you have prompted me to look again, and I've now discovered how to do it! I'll use it from now on. I'm so glad you prompted me. Thanks!
Hi Iain, you mentioned @8:06 that "at every frequency, we have two signal that are orthogonal (sin and cos)". Do you mean every signal is made of a sin and a cos? I guess not. After checking the negative freq. video, I guess you were talking about having two sinuses or cosines with opposite phase, right?
I mean that at every frequency there are two orthogonal components. e^(jwt) = cos(wt) + j sin(wt) . The cos(wt) waveform is the "real" component, and the sin(wt) waveform is the "imaginary" component. This video explains it more: "Orthogonal Basis Functions in the Fourier Transform" ua-cam.com/video/n2kesLcPY7o/v-deo.html
kindly lock your focus in the camera, it will be helpful for us. excellent explanation !!
Yes, sorry about that. I didn't know how to do it in the early days of making these videos. I've been locking the focus for the more recent videos.
This series is amazing. I was wondering if you have a lecture on Hilbert Transform?
Thanks, I'm glad you like the videos. No, I don't have a Hilbert Transform video, but it's a great suggestion. I've put it on my "to do" list.
@@iain_explains Thank you
You are an incredible teacher.
Thanks very much. I'm glad you like my explanations.
Huge thanks sir.
I'm glad it was helpful.
Thank you so much for this video
You’re welcome!
Great videos!
Hi sir,
i have been inspected fourier transform formula and i discover that fouier transform is so simple. Shift the frequency to zero and integrate one period interval. As we know, if we integrate any sinusoidal function that has nonzero frequency in one period interval we will get zero. If we pull the frequency to zero we will get non zero value and it represent the power of sinusoidal function. Fouier transform makes it, shift frequency to zero and integrate one period interval.
Excuse me Sir, I cannot understand why at 11:13 the phase of the negative frequency -f2 from negative -pi/2 becomes positive +pi/2, I'm not able to figure out why the minus before the exponential adds a pi to the phase, thanks in advance
Good question. When we expand out the brackets of the second bottom expression on the left hand side, we see that the second term is an exponential that is multiplied by -(1/2j). This is the negative of the coefficient of the first exponential. Note that -1 equals exp(i theta) when theta=pi, since exp(i theta) = cos(theta) + i sin(theta). Therefore, the "negative coefficient" of the second term, is the same as the "positive coefficient" of the first term, but just with pi added to the phase.
a nice lecture please take real data like temperature data and show us how to evaluate phase and amplitude by using fft
For what purpose would one transform the signal to the frequency domain? What are the applications?
This video gives some examples: "What is the Fourier Transform used for?" ua-cam.com/video/VtbRelEnms8/v-deo.html
Great video!
Glad you liked it
thank you
You're welcome
thank you so much for your wonderfull videos
The phase pot at the bottom right, relates to the amplitude plot that is above it. They are both for the sin(.) waveform (in the frequency domain - ie. the Fourier transform of sin(.) is a complex function - ie. the values are complex numbers - ie. they have amplitudes and phases). The top right hand plot would have its own phase plot, but I haven't drawn it.
@@iain_explains thank you so much, u are wonderful:)
Great video! I want to remind everyone of the mistake I made. Note the difference between frequency and angular frequency. (There is a coefficient difference 2pi in the inverse Fourier transform)
Yes, omega = 2pi f . It's one of the essential things that are important to know about signals and systems. This video might help with some more of those: "Essentials of Signals & Systems: Part 1" ua-cam.com/video/rw3U87aVfhc/v-deo.html
great explanation thank you so much
Glad it was helpful!
Sir, very helpful full video.😃😀👍👍👍
I'm glad you found it useful.
Namasteji.
You're welcome.
absolute legend
Glad the video was helpful.
Do you have a video that covers the "fourier slice theorem" and "radon transform"?
Sorry, not at the moment. Thanks for the suggestions. I've added them to my "to do" list.
Many thanks for this explanation. I have a query - if there are 2 frequencies(one positive and one negative) then would the amplitude of each one be half of the observed amplitude.
This video may help: "What is Negative Frequency?" ua-cam.com/video/gz6AKW-R69s/v-deo.html
ur amazing, thank you for your efforts :)
Thanks. I'm glad you like the videos.
Thank you sir
You're welcome
nice job
That's a bit harsh. I moved the paper up only a few seconds after it went off the bottom, and everything can be seen. Nobody's perfect.
So, negative frequency is only due to phase? If we had zero phase for any signal, we could just use positive frequency, right?
Well, not really. It's not "due to phase", it simply represents a complex phasor that is rotating in the negative phase direction.
In your example if you had the sin and the cosine combined in the time signal - would the amplitudes just add up in the frequency domain?
Yes, it is linear, so they add up - but it's not just the amplitudes that add - they are complex numbers in the frequency domain (as I explain from the 9:30 min mark onwards), so the phase is important, and you need to add the complex numbers (which have both amplitude and phase - not just add the amplitudes).
I am interested in Fourier series, Laplace Transform, Differential equations.
And I have read "Advanced Engineering Mathematics" by Erwin Kreyszig.
Could you recommend some other good books to study those mentioned above.
My favourite book is Oppenheim & Willsky, "Signals and Systems".
Thnx help me a lot
Glad to hear that
It seems to me the fourier transform is not a mapping from or to real functions and nor is its inverse. What function types do it and its inverse map?
Any function with finite energy.
@@iain_explains any such real function or also rational, integer and natural? By energy do you mean area under the curve?
Energy means area under the squared value of the curve. See: "Signal Power and Energy" ua-cam.com/video/7I9XEhAup4c/v-deo.html
Where can i learn about complex numbers? Maybe u have smth related?
Have you checked my webpage? Look at the Fundamental Concepts tab. iaincollings.com
Hi, can you explain why 1/(2j) = -1j/2 at 10:47. I dont understand why there is a (-) in front of j/2. Thank you
If you multiply top and bottom by j, then you get a j^2 on the bottom, which equals -1.
@@iain_explains thank u. Your lectures are amazing.
If the same frequency and amplitude orthogonal waves are added the result will be a sinewave with 45 degree phase shift. Is it right?
I think I can see what you're getting at, but you need to ask yourself what the "phase shift" is relative to (ie. "shifted" from what?). The following two waveforms are "orthogonal" to each other: +/-Asin(wt+theta) and +/-Bcos(wt+theta), for specific values of w and theta. Note that there are four possible combinations, ++, +-, -+, and --. In either of these four cases, you can add the orthogonal waveforms together and use standard trigonometric expressions to show that they can be written in the form Ccos(wt+phi). But the values of phi will be different in each of the four cases. And also the value of phi will depend on what value of theta you chose for your orthogonal waveforms. Hopefully this makes sense. This video might help: "Orthogonal Basis Functions in the Fourier Transform" ua-cam.com/video/n2kesLcPY7o/v-deo.html
Awesome
Thanks. Glad you found it helpful.
Hi, can you explain why we use gaussian filter in FSK modulation (GFSK) in next video? thank you
Thanks for the suggestion. I've added it to my "to do" list (but it's getting to be a long list, so there are a few more topics in the pipeline before I'll be able to get to it, sorry).
What is frequency response
It's the Fourier Transform of the Impulse Response of a linear time invariant (LTI) system. See: "What is a Linear Time Invariant (LTI) System?" ua-cam.com/video/5JCuqlExTvo/v-deo.html and "What is an Impulse Response?" ua-cam.com/video/WTmelRV_Yyo/v-deo.html
👍
I get it that each harmonic has a magnitude and a phase. But I don't understand how that necessitates plotting negative frequencies with the opposing phases apart from some mathematical magic. Why cant we plot both magnitude and phase for positive frequencies only? A sound wave could be represented as a sum of harmonics with different magnitudes and phases, but all in positive frequencies, right? There is nothing imaginary or negative about sound. I understand the mathematics of it but I don't understand the connection to the real world.
Excellent point! You're right, it is not necessary to employ the concept of "negative frequencies", however it's convenient to do so, and it helps visually when thinking about what's happening on the unit circle in the complex domain. Check out my video on this topic: "What is Negative Frequency?" ua-cam.com/video/gz6AKW-R69s/v-deo.html
2024.12.12 good video
after 9:21 video jump to out of focus may be he is working on imaginary axis.
For the algorithm
I did no understand the phase part from 11 mins
Perhaps this video will help: "Is Phase important in the Fourier Transform?" ua-cam.com/video/WyFO6yBQ0Cg/v-deo.html
Is this a history lesson no mathematical explanation of how we arrive from the time domain to the frequency domain no explanation of the food you serious, which is basically the representation of any periodical function
This video is focused on giving an intuitive explanation of the Fourier Transform. If you want the maths, then there are a great many textbooks that provide those details.
thank you
You're welcome
Thanks sir.
Most welcome