Alan is perhaps the best signals engineer ever. The way he teaches compels me to know more, understand and reason - with myself and others. I love the MIT courseware , thank you for this wonderful series.
It is easy to understand the property of linear system that if you put nothing in then you get nothing out. But I have trouble to understand why this property has anything to do with the causality property that the system cannot anticipate its input. Why and how are these two properties related? Another confusing part of causality of linear system is why causality means initial rest of initial conditions. Can a causal linear system have a non zero initial condition? Meaning for t < t0, its input is not zero, but can such system still be linear and causal? In another word, if you put something in, then you linearly get something out.
A linear system cannot produce an output without a corresponding input. Causality requires that the system cannot anticipate its future inputs. Zero input response (initial rest) is a consequence of causality and implies that the system's output is zero before the input is applied. A causal linear system can have non-zero initial conditions, but these conditions must not violate causality.
At 39:00, when he was speaking about the invertibility of the accumulator, he first explained that an impulse is the difference between 2 unit steps and then wrote an expression for the inverse impulse response, why did he write delta(n)-delta(n-1)=h[n]^inverse instead of writing u[n]-u[n-1]=h[n]^inverse ?
There is a reason for that, for accumulator, we need all the past values to determine the sum, but when it comes to difference we need the difference of only 2 consecutive values so we can simple multiply the coming input for the h(inverse) with impulses to get the required values and simple differentiate... for more insight integrator has limits from minus infinity to infinity but differentiator just needs it neighboring values.... Hope you find it helpful : )
As usual. great Lecture by Prof. Oppenheim. I have a question, and I hope someone here will kindly answer that. Can there be a system which linear but non-causal? I could not think of any example where a linear system is non-causal. Please shed some light.
Memoryless means that the system does not depend on previous input to determine current output. Causal means that the system depends on only current and/or past input, specifically NOT future input. Example: y[n]= x[n-1] is causal and not memoryless y[n]= x[n+1] is not causal and is memoryless y[n]= 2x[n] is causal and memoryless x[n+1] is "in the future", n is the present, thus it can't be causal.
@@crashraynor "A system is said to be memory less if its output for each value of the independent variable at a given time is dependent only on the input at that same time." Taken straight from the course textbook. Thus, y[n]=x[n+1] is not memory less. I believe the instructor speaks about such cases in the lecture about system properties.
@@pedromatias5927 this is exactly my doubt, it seems like the examples shown by the professor hint to what you are saying. I'll check the textbook for your definition, thank you for your help.
The videotaped lectures are designed to be closely integrated with the text: Oppenheim, Alan V., and A. S. Willsky. Signals and Systems. Prentice Hall, 1982. ISBN: 9780138097318. (www.amazon.com/exec/obidos/ASIN/0138097313/ref=nosim/mitopencourse-20)
Because of the difficulties the impulse function has when it is defined as a value at each time like a normal function, it is defined as an operator function along with other operational symbol functions u_1(t), u_2(t), ....These symbol functions are no longer normal functions, i.e. they do not have values defined against time, but rather operators. You no longer ask them what they are, but what they do. They are just like the addition operator ‘+’. You do not know what value ‘+’ has, but you know what exactly ‘+’ does, i.e. 1+1=2.
Alan is perhaps the best signals engineer ever. The way he teaches compels me to know more, understand and reason - with myself and others. I love the MIT courseware , thank you for this wonderful series.
im vietnammese and i fell so hard to understand =))
I was so used to hearing the lectures at 2x speed now, when I play it in normal, it literally feels like the professor is talking in slow-mo
Prof. Oppenheim, RESPECT. Your teaching is an inspiration.
I wish I had profesors like these from MIT when I was in college. Then again I wasn't at MIT.
opening music is dope
I think there's some Tron influence (1982 film)
Time travel still possible!!! Thanks Utube!
It is easy to understand the property of linear system that if you put nothing in then you get nothing out. But I have trouble to understand why this property has anything to do with the causality property that the system cannot anticipate its input. Why and how are these two properties related? Another confusing part of causality of linear system is why causality means initial rest of initial conditions. Can a causal linear system have a non zero initial condition? Meaning for t < t0, its input is not zero, but can such system still be linear and causal? In another word, if you put something in, then you linearly get something out.
A linear system cannot produce an output without a corresponding input. Causality requires that the system cannot anticipate its future inputs. Zero input response (initial rest) is a consequence of causality and implies that the system's output is zero before the input is applied. A causal linear system can have non-zero initial conditions, but these conditions must not violate causality.
Haha!
In any case, I find that watching the video again helps a great deal. Good luck!
this man is amazing
These videos are so helpful for me.Thank you sir.
In terms of Bounded Input, Bounded Output stability, I read the Wikipedia proof for discrete time systems and it makes perfect sense:
|y| = |h*x|
Old but Gold
at 22:11 it's a * not a + !!!
He said h1 convolved with h2. The * was written badly but its a *
At 39:00, when he was speaking about the invertibility of the accumulator, he first explained that an impulse is the difference between 2 unit steps and then wrote an expression for the inverse impulse response, why did he write delta(n)-delta(n-1)=h[n]^inverse instead of writing u[n]-u[n-1]=h[n]^inverse ?
There is a reason for that,
for accumulator, we need all the past values to determine the sum, but when it comes to difference we need the difference of only 2 consecutive values so we can simple multiply the coming input for the h(inverse) with impulses to get the required values and simple differentiate...
for more insight integrator has limits from minus infinity to infinity but differentiator just needs it neighboring values....
Hope you find it helpful : )
As usual. great Lecture by Prof. Oppenheim. I have a question, and I hope someone here will kindly answer that.
Can there be a system which linear but non-causal?
I could not think of any example where a linear system is non-causal. Please shed some light.
Answering myself after some brainstorming ;-)
"Moving Average Filter" is an example of linear non-causal system!
A Classic example. (y)
simply y(t)=x(t+1) is linear and non-causal.
really wondering where are you rn :)
little bit confusing......... :-(
Thank you
Anybody in 2024🤩
didn't you watch the previous lectures' videos? :P
I like the arrangement of white board ...sometime it never ends
Is the system in 19:00 has memory or memoryless?
No. It is not memoryless. It has memory.
Just to confirm, in the memory less case are we assuming that the signal is causal? Or is is being causal a property of memory less?
Memoryless means that the system does not depend on previous input to determine current output. Causal means that the system depends on only current and/or past input, specifically NOT future input. Example:
y[n]= x[n-1] is causal and not memoryless
y[n]= x[n+1] is not causal and is memoryless
y[n]= 2x[n] is causal and memoryless
x[n+1] is "in the future", n is the present, thus it can't be causal.
@@crashraynor "A system is said to be memory less if its output for each value of the independent variable
at a given time is dependent only on the input at that same time." Taken straight from the course textbook. Thus, y[n]=x[n+1] is not memory less. I believe the instructor speaks about such cases in the lecture about system properties.
@@pedromatias5927 this is exactly my doubt, it seems like the examples shown by the professor hint to what you are saying. I'll check the textbook for your definition, thank you for your help.
For a LTI system, it is true that a memory less system is also causal. For a general system, the answer may not be true.
please guys, i want the reference of this course
The videotaped lectures are designed to be closely integrated with the text: Oppenheim, Alan V., and A. S. Willsky. Signals and Systems. Prentice Hall, 1982. ISBN: 9780138097318. (www.amazon.com/exec/obidos/ASIN/0138097313/ref=nosim/mitopencourse-20)
Al is the real Howard Stark
This is it
Free Ivy League lectures ? Shit man, I'm all up in this !
im reading oppenheim's book on signals and systems.
different shirt , same dude :)
too slow... I needed to play this at 2x speed; other than that, nice lecture.
ummmn. i dont get it yet..
We have some Nintendo music :)
the later 3/4th of this lecture is very confusing
Because of the difficulties the impulse function has when it is defined as a value at each time like a normal function, it is defined as an operator function along with other operational symbol functions u_1(t), u_2(t), ....These symbol functions are no longer normal functions, i.e. they do not have values defined against time, but rather operators. You no longer ask them what they are, but what they do. They are just like the addition operator ‘+’. You do not know what value ‘+’ has, but you know what exactly ‘+’ does, i.e. 1+1=2.
LTI Systems: th-cam.com/play/PLU1h6AEhPu52EzX-KO5g5KNsbzId28Vz3.html
LTI Systems: th-cam.com/play/PLU1h6AEhPu52EzX-KO5g5KNsbzId28Vz3.html