Lecture 4, Convolution | MIT RES.6.007 Signals and Systems, Spring 2011
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- เผยแพร่เมื่อ 1 ก.ย. 2011
- Lecture 4, Convolution
Instructor: Alan V. Oppenheim
View the complete course: ocw.mit.edu/RES-6.007S11
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
The famous Alan Oppenheim. Thumbs up if you noticed his mustache is the sinc function.
Hah, and I naivly thought it is shifted cosine :D
glabka333 lol nice jokes guys :)
he's got a nice 70s groove goin on. Funk! Disco! O wait.....this was uploaded in 2011, but RECORDED in 1970! during Peak Disco Inferno......burn baby burn. wooohoooo...love it!
Ha ha. That's a good one.
Instablaster
this man is a legend. He is a legend. MIT thank you for your generous offer of education. #bravo!!
the cameraman/men for these videos probably got a very good idea of the subject
The best part of this Series is it was given in 1987, and I am in 2013 referring it. Wondering after 20 years my Son will take a visit to this site and finds my comments ..
Cheers !!
2021 xD
2021, see you in another 10 years 😂
2021 Aug
2022
2022 xD
6 dislikes. I think they are some professors because no one attends their lectures and students instead watch this guy.
You are smart.
@Beyond Oblivion your comment is platinum my friend.
Ironically my professors recommended us to follow this lecture series.
@c_a Online allowed us to do that exactly. Should i say thanks to corona? lol
I'd like to leave you with the fun and opportunity of doing that at your leisure.
Thanks to you Sir Oppenheim. An art of state courses, well done.
Alan sir your great nobody in the internet has explained convolution in this way you are a ideal person . Your are awsome. Now I got interest to do convolution. Thank you sir. Your textbook is very nice . 😀
I consider myself fortunate to have access to such useful lecture videos. I have been struggling to comprehend this topic but now I have a better grasp. Sincere thanks for uploading this video. Regards from Singapore.
Prof Oppenheim, many thanks for your great teaching.
We should learn from the best people in that field if we can... That’s what MIT OCW keep reminding me. Highly Respect to Prof Oppenheim.
I will not be surprised. This is a will never-die video . Comprehensive and straight to the point.
That opening music😂
Makes me happy😂
Thanks for the video though
Finally I understand convolution!! THANK YOU MIT!!!
best explaination of the convolution integral I have found!!
Thank you so much Prof.Alan V. Oppenheim
He go through everything so fast... this is indeed MIT speed
Thanks for posting; Im an EE major at SFSU I found this very helpful
Pof. Alan V. Oppenheim
what a charming smile before the ending!
the man's a hero.
the greatest , Alan Oppenhiem.
this guy is da bomb! thanks for the tutorial kind sir! :)
Thank u MIT, u help us learn.
Love this dr oppenheim lecture
cant believe this was made even before i was before... some people are just ahead of their time
Perfect lesson , thank you so much !
very well explained specially
the dynamic explanation of convolution
This is really beautiful .
23:45 Great explanation! My teacher didn't explain this integral thoroughly.
OMG this lecture is amazing
This guy speaks good English. I can actually learn from this.
this is taking me a huge time to wrap my head around the concept, although they are explained in a nice fashion best there is , it is still taking time
ok i think i may have got it
Very nice visualization of the convolution integral
can someone explain me how expression for x(t) and y(t) is same all though they are input and output. at 18:18.
Very well done! Viva la MIT
He is the father of signal and system 😀 cheers 👍
It represents everything about the rectangle i.e to say it gives you magnitude, area and position of the rectangle. In other words that equation and the rectangle diagram are interchangeable.
in case of time invariance system, can we write h(n-k)=h(n)?
Thank you MIT.
Amazing!
Does someone know, technically, how the convolution integral is being calculated from 34:00 until after 36:00? Is there some sort of analog computer being used?
it awesome...This lecture provides an easier understanding elaboration than his textbook.
الراجل ده عظمة اوي :D
@28:58 should not the output become zero, as soon as the h[k] crosses the extreme right point of the rectangle?
Thanks for great explination. Just I wonder what is impulse response and how we could generate such impluse and what is the amplitude for this pulse and width.
THE guru.......respect!
Old but Gold
I can't help but imagining Magnum P.I. giving a lecture on Convolution when I see that stache.
my-my, if 36:19 isn't the charging discharging of a capacitor then idk what is.
Great lectures
Thank u sir this vidio helps me lot love u mit
he's great
Great video
great lecture
I should call this guy the father of signals and systems. His book is the best as far as I know and these videos made the book more popular. I feel sad for other authors of the same field. They need to double their work to catch up this guy. Also, thanks for the cameraman. he deserves a credit. Well done MIT.
.
Bandar I'm just finding him and having a glimmer of hope of passing my signals and systems class, as my professor is on the terrible side. The guy is a walking book. Where are the professors that created the last great generation when you need them?
the book is terrible and should be used like reference book not an actual textbook meant to teach a person new to the coursework.
what a legend...
Is the demonstration done in an analog oscilloscope? Genius idea of visualization given what they have at that time.
where does Alpha comes from after getting rid of unit steps ?
Very good!
Just a recent comment passing by. This is gold.
this guy is such a gangster
Especially with that pimpin' lavender shirt
Yes
dat intro
nic video........gret work!!!!!
Where's the lecture that he discussed the properties of systems? I can't find it.
shouldnt be Interval 2: t >= 0 ?
Why would you ever want to sum any of these functions? Does the sum notation actually represent the whole signal as one formula, rather than just the sum of each sample?
who is watching this video on 2019 to understand convolution ? 😂
you're beautiful.
In 2020
I love how the way he said “strategy” just like we are solving a problem together. instead of ,this is just how the equation works , eat this shit
7:16 Shouldn't x[n] be Sigma(n=minus infinity to plus infinity) sigma( k = minus infinity to plus infinity) x[k] delta [n-k]?
Ah ok, the book I use was written by him
The guy is gold, but learning S&S from his book is extremely difficult. I had a look at S&S by MJ Roberts and quite liked it. I wonder if I'd be too far behind if I learned from this book instead.
Does any of you guys use the book by MJ Roberts?
Thanks.
Hey, i am From India, and this semester, the official book followed here is His official book, but it is too cluttered to my understanding, fortunately in the huge library, i found out that book and immidiately issued it, it is pictorially easier to understand, and after that i read your comment.
What a stache!
Could anyone please explain why h[n] at 23:00 is decaying? I think the decaying only possible if 0 < α < 1 but there is no such interval in the figure.
+Akis Stavridis
The time interval is for "n", not for "α ". He just assumed α to be between 0 and 1 for this particular example.
+Dawit Mureja Thank you for answer. Yes, he probably assumed α to be between 0 and 1 but since he did not mention or write this assumption, I was confused.
convolution :D . finally :D
i feel exactly the same. I've been trying to understand it for a while now, but I think I finally get it :)
Exact same feeling
20:03 is the wow moment
I did not understand what is h_k in the video..Can anybody please tell me?
h_k is the impulse response corresponding to the delta[n - k] impulse input. Where k goes from -inf to +inf
around the minute 44:50 appears the solution to the sum alpha^(-k), I think there is a mistake, could put some comment with the right answer please?
The book shows a similar example with that final solution, but the sum is actually alpha(k), without the minus sign
Thank you very much, these lessons are extremely useful
I have the same question!
yes i feel same!
I feel the same too, I think multiplying with alpha(k) is forgotten.
fan-frickin-tastic
how come i cant open this video full screen
well ... i got bored in the middle of the video so i went to another video
and i didn't get it then i came back here to continue and i understood every thing
thank's very very much
IT IS A FUCKIN GREAT VIDEO
CAN'T IMAGINE I FINALLY GOT IT
O.G. Alan Oppenheim
Mr Oppeheim, I have your book!
What is the meaning of weighted delayed impulse
well think of it this way a weight is the coefficient , the delayed impulse is the delta function shifted to the right/left "delayed" so you can think of a signal as individual components of x at `k` "weight", multiplied by the unit impulse -delta(n-k) -"delayed"
why n is increasing when we do summation with k in h(n-k)
n is not increasing. It is held constant based on our input.
Remember, we are now treating h(.) as a function of something; in this case, it is actually a function of k.
Let's take n = 0 (interpreted as time 0):
we have h(n-k) = h(-k), which is clearly a function of k since the n disappeared.
Now we sum across all k indexes to yield what the system would output:
y(0) = sum x(k)h(k) for all k
Notice that the sum would be very boring if the response wasn't a function of k
The background buzzing noise sure need some signal processing
Where exactly is convolution used?
Used a lot in real-time audio applications such as convolution reverb, guitar amp modelling and physical modelling of acoustic instruments.
i think Howard from Big Bang theory will look like this professor when he starts teaching (p.s. its meant in good way) nice lectures 👍
Thumbs up, to Alan v openhiem
niceee
at 44:56 i think there is an error , it should be (a^(n+1) -1)/a-1
The two expressions are the same. You may multiply the numerator and denominator by -1 and get the expression in the lecture
I'm not en engineer. Just a surgeon so bear with me. I was following this until 23:48. I would have thought that h[n-k] is h[n] shifted to the right by k. I just see that h[n] graph and imagine that it's just shifted over to the right by k. Why say that h[n] is h[k] and that h[-k] is h[k] flipped over when you could equivalently say it's just the h[n] shown with a time shift of k?
I like the idea ;-) Looks a lot simpler. But k isn't the shifting factor here. The factor k is just an integer on a infinite time-line where you can place the values of h(-k). It is the value of n that determines the shift of h(-k) via h(n-k) over this time-line. As you perhaps know, convolution is all about the overlap of 2 functions: keep one in place and shift the other one over it. Of course, it's up to you which of two function is being shifted.
@@jacobvandijk6525 so does this mean that the visualization given at 11:05 and the other visualization at 23:48 are just two different perspectives of looking at the convolution sum based on which function we choose to time shift?
@@mridulk81 I like this example very much: 27:56. Instead of reflecting h in the y-axis (what's done here), you could reflect the step-function in the y-axis and make it shift to the right. Same result.
if only my professor can explain C-T convolution as clear as him. Credit to Prof Oppenheim
P.S. he has a very calming voice
time14:09, a little confused by the words"represent the rectangle"-----represent the area of the rectangle or the magnitude of the rectangle? Seems to me all the work in this part is to introduce the delta into the expression.
It represents the magnitude of the rectangle, bc the impulse function equals (1/delta) at one particular time. if you multiply x(t)(1/delta)(delta) where t represents a value when the impulse function is equal to (1/delta) you will obtain x(t) which is the magnitude of the rectangle.
Sorry for being the only person after 6 years who have the courage to answer this question, Im studying this for the first time and enjoyed reading the comment section
same her
I think everybody studying Signals and System uses this book lol, we're using it here at Universidad Politecnica de Madrid too
We are using it too, at Istanbul Technical University.
University of Patras Greece too
The omnipresent Oppenheim, even on Brazil (Federal University of Ceará)
India too😂😂
Nazarbayev University, Kazakhstan too
it's lecture 3
ladies and gentlemen, convolution is no longer convoluted!
captain price liked this.
signals is interesting but in my experience it is the subject with the worst literature out there. Ive never read a book that actually explained things in a way that didnt assume mountains of prior knowledge. this guys book is terrible to learn from but his lectures are good. If anyone has ever found a text that isn't a total pile of shit let me know!
+Captain Rhodes I'm glad I'm not the only one who believes this about the signals literature! If you're into DSP, check out the Lyons book! All the best to you.
***** I will thanks. There is a website called complex to real dot com that has some great PDF's. Unfortunately the examples are full of mistakes but the text is pretty great. check that one out
Try the Lee Varaiya book. It is available for free online, and the practice problems, if not the chapters, are very helpful
I agree. I think Oppenheim's book is very hard to understand, but his lectures are amazing!
@@ThatOneHandsomeGamer yea hes a talented teacher but sadly his book is probably written to impress his friends
moustache impressive