Excellent. At least a decade ago I was reading Marvin Frerking’s book “Digital Signal Processing in Communication Systems” chapter 1 when this concept final clicked in my mind. He described the spectrum of a sampled signal as being periodic centered on integer multiples of the sampling frequency. For the first time in my life I felt like I really understood something important at a fundamental level. Graphically, as you have done in your video I was able to visualize the requirement for reconstruction (the Nyquist criterion). For me this is a satisfactory proof of Shannon’s sampling theorem and the Nyquist criterion rolled into one nice graphical proof. I like proofs with pictures that are rigorously correct as you have done. I don’t recall if it was presented this way when I was in college 30 and 40 years ago. It just didn’t sink in until years later.
Iain, you should really consider publishing a book on all this. I'm sure that you could singlehandedly increase the number of engineers in the country that know how to do this by a factor of ten or more. Like I seriously hope you do it, since a book written by you would be 1000 times more valuable than any book written by the textbook corporations
Thanks for your suggestion. I have thought about it, but actually I think of the collection of all my videos as comprising a "video textbook", so at the moment I'm devoting my spare time to making more videos (that reach lots of people), rather than writing a textbook (that may have a smaller reach).
@@iain_explains we will all definitely buy your book, however, the book should be also referring to each of these valuable videos. thanks a lot for these videos. I feel always I become a better engineer even by listening to very basic concept videos like this one.
@@iain_explains I know it is a little late Iain but i just wanted to say a text book would be an instant purchase if released by you, as you could include custom questions and design questions where you could reinforce knowledge by asking to make a suitable design using the concepts you had covered in end of chapter questions. Regardless, thank you for all the helpful content, hope you're well.
If you’re willing to make a video about it, a discussion of the mathematics showing how bandpass signals can often be sampled at a rate lower than Nyquist (yet still the original waveform can be picked out, if the sampling frequency is selected carefully to avoid aliasing) would be amazingly helpful. I feel like this is slightly overlooked in many places.
Thanks for the suggestion. I think I touched on it in this video (but it's been a while, so I can't remember for sure): "Sampling Bandlimited Signals: Why are the Samples "Complex"?" ruclips.net/video/JglRGRizqGM/видео.html
Very nice content Iain. It is being really helpful for preparing my signals subject. Anyway, I am missing some explanation on the signal leakage on this video, it would be something really nice to have.
I thought that the Fourier transform of a delta function was a constant frequency for all values of frequency? Is this not the case for a sequence of delta functions because there is now a "frequency" defined within the time domain? Thank you
Excellent question. Hopefully this video provides the answer you're looking for: "Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?" ruclips.net/video/ry171Hgvm-8/видео.html
Hi. I have a question. Accoding to my understanding, the FT of an impulse is a constant 1 for all frequencies in frequency domain. Then how are you taking the FT of an impulse to be an impulse?? Thanks in advance
Great question. Here's the answer: "Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?" ruclips.net/video/ry171Hgvm-8/видео.html ... and here's a visualisation of it: "Understanding Impulse Train Sampling of Discrete Time Signals" ruclips.net/video/wF2AvnncRrI/видео.html
Great video. Is this just to illustrate what aliasing is? If this was done in practice, how would you know the frequency spectrum of the sampled signal.
Wow nice explanation. But i' ve 2 questions 1)Do we need sampling to transmit analog siganal through an analog system. I mean we will transmit our message signal in analog manner like using AM/FM/PM modulation. In that case do we need sampling?? 2)Another question is there any technique to error correction and detection for analog signal??
I'm posting here because I don't understand why when we have a signal, let's say a voltage, why the units of its sampled version are Volts multiplied by Hertz and not just only Volts? It's something I've seen in my course and this is what our teacher taught us but it's doesn't make sense to me. He also taught us than the unit of the Z-Transform of this sampled signal is in Volts (whereas to me it's would have been more logical to have V.Hz for this one). It would be nice if you could help me. Thank you.
I think you'll need to ask your teacher what they meant. Volts per second does not make sense as a unit, unless you're talking about the rate of change of a voltage signal.
@@iain_explains Thanks for your fast reply. I didn't ask my question directly to my teacher because it's the holidays but i'm gonna try to send him an e-mail.
Hello Iain, thank you so much for the wonderful and clear explanations, your channel is AWESOME! Just have one question about sampling: in your example, you took a signal that has a certain BW and sampled it. What happened if you sample a pure sine wave? How the picture of the sampled signal, will look in the frequency domain? thank again!
I'm so glad to hear that you like the channel. This video will hopefully answer your question: "Typical Exam Question on Sampling" ruclips.net/video/TU-bw94Mt3Y/видео.html
thank you for really nice content! but i have a question. then, is the energy of sampling signal infinite? of course, i know it's wrong... but i don't know why that's wrong. if you don't mind, could you please tell me the reason?
Good question. The first thing to say is that the delta function does not exist in the real world. It is better to think of it as a narrow rect pulse (I've got a video coming up on this on the channel next week, so keep an eye out for that). But even then, the infinite sequence of pulses (or impulses) does not exist either. Everything in the real world occurs over a finite time window. Both of these reasons mean that the energy is not infinite in the real world. We use the theoretical ideal delta function to help us understand the real world (because the real world is a bit complicated). In any case, either way, we use the impulses in continuous-time to give us samples in discrete-time which we can manipulate in a computer or digital electronic circuit (ASIC, FPGA, GPU, etc). And in discrete-time the delta function is clearly defined, with finite energy. You might like to check out these videos for more insights: "How are Signals Reconstructed from Digital Samples?" ruclips.net/video/dD9HC1GThZY/видео.html and "Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?" ruclips.net/video/ry171Hgvm-8/видео.html
Signal sampling is a convoluted subject ;). What would be more helpful is a worked exampled of the sampled data. From Analog to digital and back to analog and sampled at there reuired frequency and below to show successful and unsuccessful recontruction. I guess if you showed everything no one would enrol.
Actually I made a new Lab for my students earlier this year doing exactly what you suggest. You've just given me the idea to make a video for this channel using that Matlab code. I'll put it on my "to do" list. Thanks for the suggestion.
Sampling is done whenever you want to store a continuous time signal in digital form. You only store the values at the sample times, so it is efficient. Although the frequency domain plot shows repeating copies, it doesn't mean the sampled signal has infinite bandwidth. You might find the following video helpful in explaining this: ruclips.net/video/P7q2YMQiat8/видео.html
But thats one wave in reality there would be a hundred or milion waves smashed on top of each others how we would sample all of them it would give inaccurate summation of amplitude of different frequencies im learning this just for curiosity but I don’t know alot i love electronics and wondering how i get obsessed compulsion of thinking about this stuff my mind can’t rest
I think the signal that was given consists of many periodic signals. By applying the Fourier transform, we can find the frequencies of those periodic signals that combine and give us the signal that we had at first. So by sampling that signal, we are already sampling all those periodic signals. I don't know if I've understood you correctly but you should look into Fourier analysis and transform. (Or just take a look at anything with the word "Fourier" in it)
Yes, that's right. It is indeed important to understand what the Fourier Transform is, and what it tells us about the signal. You might find this video useful: "What is the Fourier Transform?" ruclips.net/video/G74t5az6PLo/видео.html and you might also like to check out the other videos on the topic, listed in categorised order at this website: iaincollings.com
Excellent. At least a decade ago I was reading Marvin Frerking’s book “Digital Signal Processing in Communication Systems” chapter 1 when this concept final clicked in my mind. He described the spectrum of a sampled signal as being periodic centered on integer multiples of the sampling frequency. For the first time in my life I felt like I really understood something important at a fundamental level. Graphically, as you have done in your video I was able to visualize the requirement for reconstruction (the Nyquist criterion). For me this is a satisfactory proof of Shannon’s sampling theorem and the Nyquist criterion rolled into one nice graphical proof. I like proofs with pictures that are rigorously correct as you have done. I don’t recall if it was presented this way when I was in college 30 and 40 years ago. It just didn’t sink in until years later.
Thanks, yes I agree, graphical insights are often extremely important. I find it helps to visualise all mathematical formulas in a graphical way.
Thanks for this playlist sir. With love from Türkiye.
I'm glad you found it helpful. That's great to hear.
Iain, you should really consider publishing a book on all this. I'm sure that you could singlehandedly increase the number of engineers in the country that know how to do this by a factor of ten or more. Like I seriously hope you do it, since a book written by you would be 1000 times more valuable than any book written by the textbook corporations
Thanks for your suggestion. I have thought about it, but actually I think of the collection of all my videos as comprising a "video textbook", so at the moment I'm devoting my spare time to making more videos (that reach lots of people), rather than writing a textbook (that may have a smaller reach).
@@iain_explains That’s fair. If you ever do write one though, I’ll 100% buy it, since I’m sure it would be amazing! Thank you for everything though
@@iain_explains we will all definitely buy your book, however, the book should be also referring to each of these valuable videos. thanks a lot for these videos. I feel always I become a better engineer even by listening to very basic concept videos like this one.
@@iain_explains I know it is a little late Iain but i just wanted to say a text book would be an instant purchase if released by you, as you could include custom questions and design questions where you could reinforce knowledge by asking to make a suitable design using the concepts you had covered in end of chapter questions. Regardless, thank you for all the helpful content, hope you're well.
Thanks so much for making me understand what really means sampling a function. Cannot thank you enough Ian you are carrying me through this exam
That's great to hear. Good luck in your exams.
If you’re willing to make a video about it, a discussion of the mathematics showing how bandpass signals can often be sampled at a rate lower than Nyquist (yet still the original waveform can be picked out, if the sampling frequency is selected carefully to avoid aliasing) would be amazingly helpful. I feel like this is slightly overlooked in many places.
Thanks for the suggestion. I think I touched on it in this video (but it's been a while, so I can't remember for sure): "Sampling Bandlimited Signals: Why are the Samples "Complex"?" ruclips.net/video/JglRGRizqGM/видео.html
Awesome, straight and clear as the wind..Thanks
Glad you liked it!
Very nice content Iain. It is being really helpful for preparing my signals subject. Anyway, I am missing some explanation on the signal leakage on this video, it would be something really nice to have.
I'm glad the video was helpful. I'm not sure what you mean by "signal leakage" though, sorry.
@@iain_explains he's talking about spectral leakage
BEST EXPLANATION EVER THANK YOU
Glad you think so!
great illustration!
I thought that the Fourier transform of a delta function was a constant frequency for all values of frequency? Is this not the case for a sequence of delta functions because there is now a "frequency" defined within the time domain?
Thank you
Excellent question. Hopefully this video provides the answer you're looking for: "Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?" ruclips.net/video/ry171Hgvm-8/видео.html
Hi. I have a question. Accoding to my understanding, the FT of an impulse is a constant 1 for all frequencies in frequency domain. Then how are you taking the FT of an impulse to be an impulse??
Thanks in advance
Great question. Here's the answer: "Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?" ruclips.net/video/ry171Hgvm-8/видео.html ... and here's a visualisation of it: "Understanding Impulse Train Sampling of Discrete Time Signals" ruclips.net/video/wF2AvnncRrI/видео.html
This channel is great but somehow the volume is quite small compared to other channel even when I set the volume control at high level.
This is one of the earlier videos I made. Hopefully you find the volume on the more recent videos to be better.
All videos on youtbe are at the same level. Including this.
This was good, Thanks!
Great video. Is this just to illustrate what aliasing is? If this was done in practice, how would you know the frequency spectrum of the sampled signal.
This video might help: "Continuous Time and Discrete Time Fourier Transforms" ruclips.net/video/lLq3D-v4kPU/видео.html
Wow nice explanation.
But i' ve 2 questions
1)Do we need sampling to transmit analog siganal through an analog system. I mean we will transmit our message signal in analog manner like using AM/FM/PM modulation. In that case do we need sampling??
2)Another question is there any technique to error correction and detection for analog signal??
1) Purely analog systems do not use sampling. 2) No.
@@iain_explains
Thanks for clearing my doubts.💖
I'm posting here because I don't understand why when we have a signal, let's say a voltage, why the units of its sampled version are Volts multiplied by Hertz and not just only Volts? It's something I've seen in my course and this is what our teacher taught us but it's doesn't make sense to me.
He also taught us than the unit of the Z-Transform of this sampled signal is in Volts (whereas to me it's would have been more logical to have V.Hz for this one).
It would be nice if you could help me.
Thank you.
I think you'll need to ask your teacher what they meant. Volts per second does not make sense as a unit, unless you're talking about the rate of change of a voltage signal.
@@iain_explains Thanks for your fast reply. I didn't ask my question directly to my teacher because it's the holidays but i'm gonna try to send him an e-mail.
Hello Iain, thank you so much for the wonderful and clear explanations, your channel is AWESOME!
Just have one question about sampling: in your example, you took a signal that has a certain BW and sampled it. What happened if you sample a pure sine wave? How the picture of the sampled signal, will look in the frequency domain?
thank again!
I'm so glad to hear that you like the channel. This video will hopefully answer your question: "Typical Exam Question on Sampling" ruclips.net/video/TU-bw94Mt3Y/видео.html
@@iain_explains
Many thx I couldn't request a better explanation. amazing.
Glad it helped.
thank you for really nice content! but i have a question. then, is the energy of sampling signal infinite? of course, i know it's wrong... but i don't know why that's wrong. if you don't mind, could you please tell me the reason?
Good question. The first thing to say is that the delta function does not exist in the real world. It is better to think of it as a narrow rect pulse (I've got a video coming up on this on the channel next week, so keep an eye out for that). But even then, the infinite sequence of pulses (or impulses) does not exist either. Everything in the real world occurs over a finite time window. Both of these reasons mean that the energy is not infinite in the real world. We use the theoretical ideal delta function to help us understand the real world (because the real world is a bit complicated). In any case, either way, we use the impulses in continuous-time to give us samples in discrete-time which we can manipulate in a computer or digital electronic circuit (ASIC, FPGA, GPU, etc). And in discrete-time the delta function is clearly defined, with finite energy. You might like to check out these videos for more insights: "How are Signals Reconstructed from Digital Samples?" ruclips.net/video/dD9HC1GThZY/видео.html and "Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?" ruclips.net/video/ry171Hgvm-8/видео.html
Signal sampling is a convoluted subject ;). What would be more helpful is a worked exampled of the sampled data. From Analog to digital and back to analog and sampled at there reuired frequency and below to show successful and unsuccessful recontruction. I guess if you showed everything no one would enrol.
Actually I made a new Lab for my students earlier this year doing exactly what you suggest. You've just given me the idea to make a video for this channel using that Matlab code. I'll put it on my "to do" list. Thanks for the suggestion.
can you please discus the requirement of sampling since it clearly occupies enormous bandwidth in frequency domain.
Sampling is done whenever you want to store a continuous time signal in digital form. You only store the values at the sample times, so it is efficient. Although the frequency domain plot shows repeating copies, it doesn't mean the sampled signal has infinite bandwidth. You might find the following video helpful in explaining this: ruclips.net/video/P7q2YMQiat8/видео.html
Thankអរគុណ👏
I'm glad you found the video helpful.
But thats one wave in reality there would be a hundred or milion waves smashed on top of each others how we would sample all of them it would give inaccurate summation of amplitude of different frequencies im learning this just for curiosity but I don’t know alot i love electronics and wondering how i get obsessed compulsion of thinking about this stuff my mind can’t rest
I think the signal that was given consists of many periodic signals. By applying the Fourier transform, we can find the frequencies of those periodic signals that combine and give us the signal that we had at first. So by sampling that signal, we are already sampling all those periodic signals. I don't know if I've understood you correctly but you should look into Fourier analysis and transform. (Or just take a look at anything with the word "Fourier" in it)
Yes, that's right. It is indeed important to understand what the Fourier Transform is, and what it tells us about the signal. You might find this video useful: "What is the Fourier Transform?" ruclips.net/video/G74t5az6PLo/видео.html and you might also like to check out the other videos on the topic, listed in categorised order at this website: iaincollings.com