Lecture 4, Convolution | MIT RES.6.007 Signals and Systems, Spring 2011

Lecture 4, Convolution
Instructor: Alan V. Oppenheim
View the complete course: ocw.mit.edu/RES...
License: Creative Commons BY-NC-SA
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[@otsilekgaladua5485]

this man is a legend. He is a legend. MIT thank you for your generous offer of education. #bravo!!

[@aderants]

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 !!

[@ahad1709]

2021 xD

[@harisirfanbutt]

2021, see you in another 10 years 😂

[@intelligentdonkey6982]

2021 Aug

[@tahmid1847]

2022

[@lounes9777]

2022 xD

[@ConsciousnessIsMyGod]

The famous Alan Oppenheim. Thumbs up if you noticed his mustache is the sinc function.

[@glabka333]

Hah, and I naivly thought it is shifted cosine :D

[@boughouabdou605]

glabka333 lol nice jokes guys :)

[@klam77]

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!

[@javijee_]

Ha ha. That's a good one.

[@leandrogage9409]

Instablaster

[@goharkay]

the cameraman/men for these videos probably got a very good idea of the subject

[@bandar1606]

6 dislikes. I think they are some professors because no one attends their lectures and students instead watch this guy.

[@univuniveral9713]

You are smart.

[@manideepp2229]

@Beyond Oblivion your comment is platinum my friend.

[@unknownuser927]

Ironically my professors recommended us to follow this lecture series.

[@amit-mishra]

@c_a Online allowed us to do that exactly. Should i say thanks to corona? lol

[@lokeshm2583]

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 . 😀

[@samuelleung9930]

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.

[@rgseven6557]

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.

[@boughouabdou605]

Thanks to you Sir Oppenheim. An art of state courses, well done.

[@probono2876]

Prof Oppenheim, many thanks for your great teaching.

[@josechemist]

I will not be surprised. This is a will never-die video . Comprehensive and straight to the point.

[@Lycheeee11]

Finally I understand convolution!! THANK YOU MIT!!!

[@VarunKumar-ir6wd]

I'd like to leave you with the fun and opportunity of doing that at your leisure.

[@LennyGrayGuiltless]

Thanks for posting; Im an EE major at SFSU I found this very helpful

[@storgerbenevolent5678]

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

[@storgerbenevolent5678]

ok i think i may have got it

[@georgeyu7987]

He go through everything so fast... this is indeed MIT speed

[@OmarChida]

Pof. Alan V. Oppenheim

[@imjisooimok1826]

That opening music😂 Makes me happy😂 Thanks for the video though

[@EngBandar1]

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.

[@drtgyjk]

.

[@dopier12]

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?

[@Bluddyshadowhell]

the book is terrible and should be used like reference book not an actual textbook meant to teach a person new to the coursework.

[@chinnu349]

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.

[@cpeter9569]

best explaination of the convolution integral I have found!!

[@emrahtokalac1721]

Thank you so much Prof.Alan V. Oppenheim

[@frankliou3609]

what a charming smile before the ending!

[@RomyvanEs]

the man's a hero.

[@karankhatwani8987]

the greatest , Alan Oppenhiem.

[@roros2512]

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

[@ze2411]

I have the same question!

[@storgerbenevolent5678]

yes i feel same!

[@beytulk]

I feel the same too, I think multiplying with alpha(k) is forgotten.

[@nikshepbangera5416]

cant believe this was made even before i was before... some people are just ahead of their time

[@TheReligiousCrap]

23:45 Great explanation! My teacher didn't explain this integral thoroughly.

[@LucasAmorimPlus]

I can't help but imagining Magnum P.I. giving a lecture on Convolution when I see that stache.

[@area51xi]

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?

[@jacobvandijk6525]

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.

[@mridulk81]

@@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?

[@jacobvandijk6525]

@@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.

[@Gman2486]

This guy speaks good English. I can actually learn from this.

[@rishavkumar9288]

He is the father of signal and system 😀 cheers 👍

[@dabulls1g]

my-my, if 36:19 isn't the charging discharging of a capacitor then idk what is.

[@TheGi0gio]

this guy is da bomb! thanks for the tutorial kind sir! :)

[@DF-ss5ep]

Very nice visualization of the convolution integral

[@alimousvi9846]

Thank u MIT, u help us learn.

[@glaurung78]

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?

[@el_witcher]

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.

[@guruG509]

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.

[@thesecrethero9901]

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.

[@dawitmureja2228]

+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.

[@thesecrethero9901]

+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.

[@saswatisil8886]

@28:58 should not the output become zero, as soon as the h[k] crosses the extreme right point of the rectangle?

[@aggressivetourist1818]

OMG this lecture is amazing

[@stevenan93]

this guy is such a gangster

[@roymarshall_]

Especially with that pimpin' lavender shirt

[@rockingbalu3652]

Yes

[@boshooda1941]

dat intro

[@fardeszx]

it awesome...This lecture provides an easier understanding elaboration than his textbook.

[@storgerbenevolent5678]

at 44:56 i think there is an error , it should be (a^(n+1) -1)/a-1

[@giacomodemarie2497]

The two expressions are the same. You may multiply the numerator and denominator by -1 and get the expression in the lecture

[@jacobvandijk6525]

@ 33:57 In my opinion, the lowest graph should not begin at 0 (but at 1 (= e^0)). The same thing here: 35:33. Just compare it with the correct graph of the discrete case: 26:58. Even mr Oppenheim isn't flawless ;-) Nice animation though.

[@AlexAlex-fo9gt]

kzbin.info/www/bejne/iX_Hf5lpotWlqLc This is example of calculation. And in this example values start from 0.

[@vivekrai1974]

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]?

[@TANVEER991164]

very well explained specially the dynamic explanation of convolution

[@abdoaboganima]

الراجل ده عظمة اوي :D

[@masonhung7061]

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

[@superparko1]

Just a recent comment passing by. This is gold.

[@RohitPandey127]

can someone explain me how expression for x(t) and y(t) is same all though they are input and output. at 18:18.

[@Dr2quan]

20:03 is the wow moment

[@damny0utoobe]

Love this dr oppenheim lecture

convolution :D . finally :D

[@vg5028]

i feel exactly the same. I've been trying to understand it for a while now, but I think I finally get it :)

[@nagarajuchukkala9538]

Exact same feeling

[@makishimashogo1804]

I did not understand what is h_k in the video..Can anybody please tell me?

[@vg5028]

h_k is the impulse response corresponding to the delta[n - k] impulse input. Where k goes from -inf to +inf

[@khaben6986]

who is watching this video on 2019 to understand convolution ? 😂

[@boshooda1941]

you're beautiful.

[@manideepp2229]

In 2020

[@oskarmeister]

The background buzzing noise sure need some signal processing

[@abdelrahmanyasser5720]

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

[@abdelrahmanyasser5720]

IT IS A FUCKIN GREAT VIDEO CAN'T IMAGINE I FINALLY GOT IT

[@jerusheng]

Is the demonstration done in an analog oscilloscope? Genius idea of visualization given what they have at that time.

[@LuckFx]

I think everybody studying Signals and System uses this book lol, we're using it here at Universidad Politecnica de Madrid too

[@omega7377]

We are using it too, at Istanbul Technical University.

[@maheryagub]

University of Patras Greece too

[@manoelnt0]

The omnipresent Oppenheim, even on Brazil (Federal University of Ceará)

[@imjisooimok1826]

India too😂😂

[@ПетрИванович-л6ж]

Nazarbayev University, Kazakhstan too

[@moatacemaskar7313]

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.

[@AnasAhmad7]

This is really beautiful .

[@tintindear000]

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.

[@superparko1]

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.

[@superparko1]

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

[@azstudioproductions]

Perfect lesson , thank you so much !

[@adarshabbigeriadarshabbige8004]

Thank u sir this vidio helps me lot love u mit

[@elmotivoso85]

Ah ok, the book I use was written by him

[@socratesuffer2765]

where does Alpha comes from after getting rid of unit steps ?

[@mohamedessam1397]

Old but Gold

[@Captain_Rhodes]

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!

[@adityatyagi4009]

+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.

[@Captain_Rhodes]

***** 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

[@atifmmahmud]

Try the Lee Varaiya book. It is available for free online, and the practice problems, if not the chapters, are very helpful

[@ThatOneHandsomeGamer]

I agree. I think Oppenheim's book is very hard to understand, but his lectures are amazing!

[@Captain_Rhodes]

@@ThatOneHandsomeGamer yea hes a talented teacher but sadly his book is probably written to impress his friends

[@pyrocolada]

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?

[@haoyuan92]

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

[@shashibhushansharma1383]

in case of time invariance system, can we write h(n-k)=h(n)?

[@klam77]

THE guru.......respect!

[@makishimashogo1804]

What is the meaning of weighted delayed impulse

[@MoutasemMohammad]

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"

[@SameerSk]

Thank you MIT.

[@SatyamMishraBEE]

Great lectures

[@AllHailAkemi]

Mr Oppeheim, I have your book!

[@chaitanya.shankar]

Where exactly is convolution used?

[@amber1862]

Used a lot in real-time audio applications such as convolution reverb, guitar amp modelling and physical modelling of acoustic instruments.

[@ManojKumar-el9bq]

why n is increasing when we do summation with k in h(n-k)

[@aSeaofTroubles]

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

[@SmartSula]

Where's the lecture that he discussed the properties of systems? I can't find it.

[@fazlanpera]

Very well done! Viva la MIT

[@RAGHAVENDRASINGH17]

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 👍

[@andrewdavis6191]

Amazing!

[@whodaFru4551]

shouldnt be Interval 2: t >= 0 ?

[@venkatasaketramgoteti8726]

great lecture

[@Giesel47]

what a legend...

[@TheAllboutwin]

What a stache!

[@ranjeetmishra8600]

nic video........gret work!!!!!

[@TheRonaldinho80R10]

Great video

[@jj1221ify]

fan-frickin-tastic

[@owaismansoori1498]

he's great

[@osamaasif9601]

Thumbs up, to Alan v openhiem

[@appleraja]

how come i cant open this video full screen

Very good!

[@zf164]

O.G. Alan Oppenheim

[@computerdynamo]

Something about his delivery reminds me of Christopher Walken.

[@FahimKhan-vd8yp]

ladies and gentlemen, convolution is no longer convoluted!

[@strayon7333]

captain price liked this.

[@karimkhan1312]

EXCELLENT , CONCEPT CLEARED ; THANK U -- AMARJIT ; ADVOCATE DELHI HIGH COURT ; INDIA

[@halil_candan]

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