I had the privilege of being an intern with Dr. Thomas G. Stockham Jr. one of the modern pioneers of DSP, at the University of Utah in the 80s. I have never had a teacher who resonated better with me than him. We were a month into doing Fourier Transforms graphically before he derived the equation. When he did it took about 15 minutes at the end of the class and I understood it so well. Your style of teaching is so similar to his, I truly enjoy your videos. Thank you.
hello sir how are you ? i have cracked my interview after learning concepts from you now i am assistant professor at government owned engineering college a thanks is not enough for you sir you are a magician as i always say cheers to you sir 😊
Thank you so much for these refreshing videos Iain....I have learnt so much from your teaching style and cleared a lot of concepts in digital communication!!
Such a great video! Its so fun to watch these lectures. I especially like random comments like "inverted in time & complex conjugate." Its like the thought never occurred to me that that's what a complex conjugated does, but i can imagine that flipping the sign of the imaginary component in a complex exponential just changes the direction its rotating over time -> time reversal! Super cool.
Unfortunately, I am not able to relate the "Square Root Raised Cosine" with transmitted symbols or signals in SC-FDMA and OFDM. I have looked at other comments of this video, and I saw there were three similar questions. So I assume, after watching other related videos of you, it is reasonable to request you please create a clarification video about: "What is the relation between raised cosine pulse shaping and OFDM?" I must thank you for all the great videos that I learn a lot from.
The issue that you've sidestepped (on purpose) is that a root raised-cosine filter is not realizable (because its impulse response is not causal). How does one implement a root raised-cosine filter in practice?
Yes. Great point. In practice it is necessary to truncate the pulse in the time domain, and implement (incur) a delay of as many symbol periods as the length of the truncated tail. Nothing comes for free! 😁
Hello Iain, thanks for the great videos, I suggest you to all of my classmates! I wonder if you can suggest me a good book about communications which explains these topics close to your teaching way?
That's great to hear. Thanks for recommending my videos. Unfortunately I don't know of a good textbook that explains things this way - which is partly what motivated me to start making these videos in the first place. I think of these videos as my "textbook".
Great video as usual :-). One question, though! Where in the receiver chain is this matched filter [Hr(t)] located? From your sheet, it looks like this is located before the ADC as y(t) ti converted to y(k) after this filter. I come from RF background and I haven't seen any matched filter before ADC. We have an anti-aliasing filter but not the matching filter. Can you please elaborate if possible.
It depends on the implementation. Consider the most basic case, where you are sending square waveforms mixed up to a carrier. If your ADC in the receiver is sampling at the symbol rate, then the down conversion mixer (in the receiver) combined with the symbol-period integrator in the ADC, are performing the "matching". This is a version of the "correlator" implementation of the matched filter. The oscillator in the mixer is "matched" to the input waveform (ie. the have the same frequency, and phase offset).
Try now, I've just uploaded it again (not sure why it didn't work before, sorry). It's really a Summary Sheet, not a Worksheet. I initially had intentions of producing worksheets, but I haven't had enough spare time. Thanks for alerting me to the upload issue.
Thank you for your great videos! I have some quesions, and would appreciate it if you could answer. Why do we split the raised cosine in the transmitter and the receiver? Couldn't we just put an RC filter in the transmitter instead of putting RRC filters in both the transmitter and the receiver? Also, how does the receiver know what roll-off factor to choose for its RRC filter?
You need to have a filter at each end of the link, because the link is a real continuous-time channel. For more explanation on this, see: "What is a Matched Filter?" czcams.com/video/Ci-EjiMJo3I/video.html And the choice of the roll-off factor is a design choice based on a number of factors, including how the timing acquisition is done, how much bandwidth is available, and what data rate you're trying to achieve, ... amongst other things.
Thank you so much,Iain! Can you tell me what the signal formula for the matched filter is if the transmit filter is a Gaussian filter used in MSK.I can't find the answer to this question online
The Matched filter impulse response is the complex conjugate of the time reversed transmit filter (by definition). This video will hopefully help: "What is a Matched Filter?" czcams.com/video/Ci-EjiMJo3I/video.html
In OFDM systems, the symbol shape is pretty random as it is composed of multiple individually modulated signals. So, in that case is it possible to design a matched filter for OFDM symbols or this applies to the underlying symbol shape that modulates each OFDM carrier.
The pulse shaping is done at the sample rate in OFDM (not the symbol rate). For example, if the OFDM "symbol" consists of 1024 "time domain samples", then each sample needs to be sent with a pulse shape.
Prof thank you so much for these videos! I've been playing with digital comms for one project of mine, and I got a question, if I may. I've been trying to buld a digital transmitter "from the scratch". In practice, how one would implement the R.C. filter in a digital system? My guess is in the form of a FIR or IIR filter stored in the memory, but I can't get any glimpse regarding how one would implement the convolution between such filter and the impulse sequence s(t) into a digital unit (say, a microcontroller). I hope you can comment something on this. Thank you so much!
Great question. The convolution would need to be done at a high rate (compared to the symbol rate) and can be done (for each of the in-phase and quadrature components) by copying the R.C. impulse response (at the high rate) into the output vector, centred on each digital symbol time, and multiplied by the symbol's amplitude (in-phase or quadrature, respectively). You then need a high rate DAC. These videos might help: "Discrete Time Convolution Example" czcams.com/video/KAOJsqCyd5Y/video.html , "How are Signals Reconstructed from Digital Samples?" czcams.com/video/dD9HC1GThZY/video.html and "What is a 1-Bit DAC and How Does it Work?" czcams.com/video/3R8ipTHb9xQ/video.html
Thanks for the video 1-if pulse shaping cancels the isi in a dispersive channel then why do we need ofdm ? 2- in awgn channel (for ex wired comm ) do we need a pulse shaping satisfying Nyquist criterion for zero isi ?
Pulse shaping only cancels the ISI _fully_ in certain circumstances (see the video: "How to Avoid ISI in Digital Communications: Nyquist Zero ISI Theorem" czcams.com/video/sgyTlI9BsKc/video.html). When the transmitter does not know the channel transfer function (which is often the case in wireless communications with time varying channels), then it cannot _predistort_ the signal in the optimal way to avoid ISI, and then equalisation needs to be done at the receiver. This is where OFDM is good, since it makes the equalisation task easy at the receiver. See "How does OFDM Overcome ISI?" czcams.com/video/xcQ6rtIXv6M/video.html
@@iain_explains Thanks but 1- what about my second question above ? 2-it is mentioned that the tx practically doesn't know the channel but the tx can know the channel using reference signals this is in all the 3gpp standards I know about Moreover it is mentioned that the channel is time varying yes indeed but only after the coherence period So I still do not get why pulse shaping for zero isi is not used instead of ofdm
Hi , when you say that s(t) is a way to send digital samples , by using impulses , I want to understand how those impulses generated in practice .In practice it would not be possible to generate a impulse to represent digital 1 / 0 . in fact it must be some form of rectangular function . so the question is in reality what is a impulse response as we can never generate a impulse in time domain .
Excellent point. Yes, in practice we need to find some way to implement the equivalent of the symbol transmit filter. This can be done, for example in the case of BPSK, by using a crystal oscillator (for the carrier signal), and a simple switching circuit (to generate a square wave signal that changes between -1V and +1V depending on the digital data), and then multiplying them together with an electronic multiplier circuit.
@@iain_explains Thanks for the explanation you provided . I did understand your point.However for the sake of clarity i would like to clarify certain things with respect to this video . So what I understand is that we are trying to model the impulse response of the transmit filter and in this case we find that if we have a time constrained raised cosine then we have better frequency domain characteristics which prevent interference. Now what I understand is that we are actually not referring to impulse response but a symbol response Of the transmit filter , as we will have a BPSK signal for example . I have one doubt here . So the carrier which you are referring here , Crystal oscillator, will that multiply the response of the filter in time domain ?. So I am trying to imagine a waveform that carrier frequency ( cosine function in time ) multiplied by the raised cosine at the transmitter. Am I imagining it correctly?
Thanks for the video. A question here: the OFDM subcarriers look like sinc functions and spread over the whole bandwidth. Will that be a problem or what do I miss?
Sorry, I'm not exactly sure what you're asking, because this video does not have OFDM in it. But anyway, perhaps this video will help: "How are Data Rate and Bandwidth Related?" czcams.com/video/ZBSvMbO0mPQ/video.html
@@iain_explains Sorry for the unclear question. I mean at 6:51, you mentioned that the sidelobe could go forever but we do not have infinite bandwidth. I want to ask if it is the same case for OFDM signal? Or in OFDM there is no such issue because the sinc functions of each subcarrier are orthogonal to each other?
Yes it's the same for OFDM. Each subcarrier in OFDM is a sinc function. this video explains it more: "OFDM Waveforms" czcams.com/video/F6B4Kyj2rLw/video.html
That's something that you can easily find on Wikipedia. I prefer to focus my videos on _understanding_ . The details of the maths can always be found in textbooks/Wikipedia/etc. Too many maths details in a video detract from the understanding, and put people to sleep (including me!)
Great explanation sir, At @6:30 in the video ==> How are Data Rate and Bandwidth Related? ( czcams.com/video/ZBSvMbO0mPQ/video.html ) .. The time limited wave form you discussed is similar to what you discussed in this video * Raised cosine waveform) ?
Very clear and compact explanation. Although i already teach DSP and Digital Comms , this gave me a brand new insight. A BIG thank you from Greece !!!
I'm so glad it was helpful!
This is an amazing channel!
Thanks. I'm glad you're finding the videos helpful, and I really appreciate your nice comment.
Thank you so much for making these videos, Iain! You make it a lot easier to understand than my textbooks
Glad you like them!
I had the privilege of being an intern with Dr. Thomas G. Stockham Jr. one of the modern pioneers of DSP, at the University of Utah in the 80s. I have never had a teacher who resonated better with me than him. We were a month into doing Fourier Transforms graphically before he derived the equation. When he did it took about 15 minutes at the end of the class and I understood it so well. Your style of teaching is so similar to his, I truly enjoy your videos. Thank you.
Wow, that is high praise indeed. I really appreciate your comments, and I'm so glad you enjoy my videos.
great work. . . .its hard to find such a good explanation of the fundamental concepts of these topics elsewhere. thanks a lot
Glad you liked it
The best video ever regarding digital communications. No doubt!
Thanks so much. I'm glad you liked it.
best teacher that I ever seen. thank you so much
Thanks for your nice comment. Glad you're finding the videos helpful.
Thank you for breaking down the time domain and frequency domain singals with pros and cons regarding the inter symbol interference.
I'm glad it was helpful. Thanks for your comment.
hello sir how are you ? i have cracked my interview after learning concepts from you now i am assistant professor at government owned engineering college a thanks is not enough for you sir you are a magician as i always say cheers to you sir 😊
That's wonderful news. Congratulations! I'm so glad to hear it.
@@iain_explains if life and time will permit I would like to meet you once 😊
That will be nice. Perhaps at a research conference in future.
Thank you so much for these refreshing videos Iain....I have learnt so much from your teaching style and cleared a lot of concepts in digital communication!!
That's great to hear. I'm glad you've found the videos helpful.
the explanation was really seamless and easy to grasp. Thanks prof!
Glad it was helpful!
Worth it watch entire video.
Such a great video! Its so fun to watch these lectures. I especially like random comments like "inverted in time & complex conjugate." Its like the thought never occurred to me that that's what a complex conjugated does, but i can imagine that flipping the sign of the imaginary component in a complex exponential just changes the direction its rotating over time -> time reversal! Super cool.
Glad you liked the video, and I'm especially glad you like the insights I try to add along the way.
Unfortunately, I am not able to relate the "Square Root Raised Cosine" with transmitted symbols or signals in SC-FDMA and OFDM. I have looked at other comments of this video, and I saw there were three similar questions. So I assume, after watching other related videos of you, it is reasonable to request you please create a clarification video about: "What is the relation between raised cosine pulse shaping and OFDM?" I must thank you for all the great videos that I learn a lot from.
Have you seen this video? "How are OFDM Sub Carrier Spacing and Time Samples Related?" czcams.com/video/knjeXo3VZvc/video.html
Good explaination...
Thank u soo much sir for grt explaination
you save my life!
The issue that you've sidestepped (on purpose) is that a root raised-cosine filter is not realizable (because its impulse response is not causal). How does one implement a root raised-cosine filter in practice?
Yes. Great point. In practice it is necessary to truncate the pulse in the time domain, and implement (incur) a delay of as many symbol periods as the length of the truncated tail. Nothing comes for free! 😁
Hello Iain, thanks for the great videos, I suggest you to all of my classmates! I wonder if you can suggest me a good book about communications which explains these topics close to your teaching way?
That's great to hear. Thanks for recommending my videos. Unfortunately I don't know of a good textbook that explains things this way - which is partly what motivated me to start making these videos in the first place. I think of these videos as my "textbook".
Great video as usual :-). One question, though! Where in the receiver chain is this matched filter [Hr(t)] located? From your sheet, it looks like this is located before the ADC as y(t) ti converted to y(k) after this filter. I come from RF background and I haven't seen any matched filter before ADC. We have an anti-aliasing filter but not the matching filter. Can you please elaborate if possible.
It depends on the implementation. Consider the most basic case, where you are sending square waveforms mixed up to a carrier. If your ADC in the receiver is sampling at the symbol rate, then the down conversion mixer (in the receiver) combined with the symbol-period integrator in the ADC, are performing the "matching". This is a version of the "correlator" implementation of the matched filter. The oscillator in the mixer is "matched" to the input waveform (ie. the have the same frequency, and phase offset).
thank you very much the video that i am looking for
Glad I could help
Thank you !
You're welcome!
Hi Iain, great video. The pdf worksheet of this class isn't allowing download. Can you take a look on it please? Thanks!
Try now, I've just uploaded it again (not sure why it didn't work before, sorry). It's really a Summary Sheet, not a Worksheet. I initially had intentions of producing worksheets, but I haven't had enough spare time. Thanks for alerting me to the upload issue.
Iain Explains Signals and Systems The summary sheet works very well. It’s a good way to have your notes without taking screenshots. Great work!
Greetings, I am teaching the Digital Communication course and benefit from your explanations.
Great. I'm glad the videos are helpful. Let me know if you think there are new things I should cover.
Very good video!
Glad you liked it!
Thank you for your great videos! I have some quesions, and would appreciate it if you could answer.
Why do we split the raised cosine in the transmitter and the receiver? Couldn't we just put an RC filter in the transmitter instead of putting RRC filters in both the transmitter and the receiver? Also, how does the receiver know what roll-off factor to choose for its RRC filter?
You need to have a filter at each end of the link, because the link is a real continuous-time channel. For more explanation on this, see: "What is a Matched Filter?" czcams.com/video/Ci-EjiMJo3I/video.html And the choice of the roll-off factor is a design choice based on a number of factors, including how the timing acquisition is done, how much bandwidth is available, and what data rate you're trying to achieve, ... amongst other things.
Great Work. Thank you, sir..
Glad you like the videos.
Thank you so much,Iain! Can you tell me what the signal formula for the matched filter is if the transmit filter is a Gaussian filter used in MSK.I can't find the answer to this question online
The Matched filter impulse response is the complex conjugate of the time reversed transmit filter (by definition). This video will hopefully help: "What is a Matched Filter?" czcams.com/video/Ci-EjiMJo3I/video.html
In OFDM systems, the symbol shape is pretty random as it is composed of multiple individually modulated signals. So, in that case is it possible to design a matched filter for OFDM symbols or this applies to the underlying symbol shape that modulates each OFDM carrier.
The pulse shaping is done at the sample rate in OFDM (not the symbol rate). For example, if the OFDM "symbol" consists of 1024 "time domain samples", then each sample needs to be sent with a pulse shape.
Prof thank you so much for these videos! I've been playing with digital comms for one project of mine, and I got a question, if I may.
I've been trying to buld a digital transmitter "from the scratch".
In practice, how one would implement the R.C. filter in a digital system? My guess is in the form of a FIR or IIR filter stored in the memory, but I can't get any glimpse regarding how one would implement the convolution between such filter and the impulse sequence s(t) into a digital unit (say, a microcontroller).
I hope you can comment something on this. Thank you so much!
Great question. The convolution would need to be done at a high rate (compared to the symbol rate) and can be done (for each of the in-phase and quadrature components) by copying the R.C. impulse response (at the high rate) into the output vector, centred on each digital symbol time, and multiplied by the symbol's amplitude (in-phase or quadrature, respectively). You then need a high rate DAC. These videos might help: "Discrete Time Convolution Example" czcams.com/video/KAOJsqCyd5Y/video.html , "How are Signals Reconstructed from Digital Samples?" czcams.com/video/dD9HC1GThZY/video.html and "What is a 1-Bit DAC and How Does it Work?" czcams.com/video/3R8ipTHb9xQ/video.html
@@iain_explains thank for the precious info!
Thanks for the video
1-if pulse shaping cancels the isi in a dispersive channel then why do we need ofdm ?
2- in awgn channel (for ex wired comm ) do we need a pulse shaping satisfying Nyquist criterion for zero isi ?
Pulse shaping only cancels the ISI _fully_ in certain circumstances (see the video: "How to Avoid ISI in Digital Communications: Nyquist Zero ISI Theorem" czcams.com/video/sgyTlI9BsKc/video.html). When the transmitter does not know the channel transfer function (which is often the case in wireless communications with time varying channels), then it cannot _predistort_ the signal in the optimal way to avoid ISI, and then equalisation needs to be done at the receiver. This is where OFDM is good, since it makes the equalisation task easy at the receiver. See "How does OFDM Overcome ISI?" czcams.com/video/xcQ6rtIXv6M/video.html
@@iain_explains
Thanks but
1- what about my second question above ?
2-it is mentioned that the tx practically doesn't know the channel but the tx can know the channel using reference signals this is in all the 3gpp standards I know about
Moreover it is mentioned that the channel is time varying yes indeed but only after the coherence period
So I still do not get why pulse shaping for zero isi is not used instead of ofdm
Hi , when you say that s(t) is a way to send digital samples , by using impulses , I want to understand how those impulses generated in practice .In practice it would not be possible to generate a impulse to represent digital 1 / 0 . in fact it must be some form of rectangular function . so the question is in reality what is a impulse response as we can never generate a impulse in time domain .
Excellent point. Yes, in practice we need to find some way to implement the equivalent of the symbol transmit filter. This can be done, for example in the case of BPSK, by using a crystal oscillator (for the carrier signal), and a simple switching circuit (to generate a square wave signal that changes between -1V and +1V depending on the digital data), and then multiplying them together with an electronic multiplier circuit.
@@iain_explains Thanks for the explanation you provided . I did understand your point.However for the sake of clarity i would like to clarify certain things with respect to this video . So what I understand is that we are trying to model the impulse response of the transmit filter and in this case we find that if we have a time constrained raised cosine then we have better frequency domain characteristics which prevent interference. Now what I understand is that we are actually not referring to impulse response but a symbol response Of the transmit filter , as we will have a BPSK signal for example . I have one doubt here . So the carrier which you are referring here , Crystal oscillator, will that multiply the response of the filter in time domain ?. So I am trying to imagine a waveform that carrier frequency ( cosine function in time ) multiplied by the raised cosine at the transmitter. Am I imagining it correctly?
Thanks for the video. A question here: the OFDM subcarriers look like sinc functions and spread over the whole bandwidth. Will that be a problem or what do I miss?
Sorry, I'm not exactly sure what you're asking, because this video does not have OFDM in it. But anyway, perhaps this video will help: "How are Data Rate and Bandwidth Related?" czcams.com/video/ZBSvMbO0mPQ/video.html
@@iain_explains Sorry for the unclear question. I mean at 6:51, you mentioned that the sidelobe could go forever but we do not have infinite bandwidth. I want to ask if it is the same case for OFDM signal? Or in OFDM there is no such issue because the sinc functions of each subcarrier are orthogonal to each other?
Yes it's the same for OFDM. Each subcarrier in OFDM is a sinc function. this video explains it more: "OFDM Waveforms" czcams.com/video/F6B4Kyj2rLw/video.html
Great videos
Glad you like them!
Ok, but what is the closed form for a square-root-raised-cosine function?
That's something that you can easily find on Wikipedia. I prefer to focus my videos on _understanding_ . The details of the maths can always be found in textbooks/Wikipedia/etc. Too many maths details in a video detract from the understanding, and put people to sleep (including me!)
Just looked it up, and that is one complicated function!
How do we find factor 't' when we use h(T) in Raised Cosine Filter?
I think you might be confusing things. h(T) is the value of the function h(t) evaluated at the time t=T.
great video, but the pen is very harsh on the ears
Thanks for pointing it out. I hadn't noticed, sorry. I've been using a different pen recently, which makes less noise (now that I think about it).
Great explanation sir,
At @6:30 in the video ==> How are Data Rate and Bandwidth Related? ( czcams.com/video/ZBSvMbO0mPQ/video.html ) .. The time limited wave form you discussed is similar to what you discussed in this video * Raised cosine waveform) ?
Yes, that's right.