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
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!
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 !!
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.
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 . 😀
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.
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
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.
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?
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?
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.
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?
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
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.
+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.
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
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
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"
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
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.
