That delta(t-T) repeatedly confused me, but Iain shows that it's the variable t that (as I think of it) leads and moves over time (the variability based in time) to the constant at set moment T. Then, the delta "strikes" at time t=T.
All the content you are provide was just amazing but i have doubt is that you said that amplitude is infinity at t=0 but also you said that at t=0 height is 1 why?
Ah, good point. Technically, the delta function has an infinite amplitude, and infinitesimally narrow width. The important thing is the area that results from multiplying the amplitude with the width. We draw delta functions with a vertical arrow, and often we draw the height of the arrow to indicate the area. Eg. a delta function with area =1 would be drawn half the height of a delta function with area =2. So sometimes people refer to the "height" of the delta function, when they actually mean the "area".
I'm not sure why you think this. I'm just showing some examples, so I could choose to integrate over any range I like. Maybe you are thinking that "time" can only be positive? If so, then it's important to understand that the "zero" time in any graph is simply a reference time, so negative time simply means the time before the reference time. And also it's important to understand that I could have used any symbol for the "x-axis" - it didn't need to be "t", and it didn't need to represent "time". It is just the variable for the function. The properties of delta functions hold for any "x-axis" variable that takes continuous values (eg. distance, height, length, temperature, acceleration, ... whatever)
What I do not get is when the variable t is not 5, the function is equal to 0. In the last example, how do they add up to Ax(5)? When t is larger than 5, the function takes on the value of zero. So if we multiply it with x(t=5), isn't it equal to 0?
For all values of t that do not equal 5, the function x(t)delta(t-5) = 0. So when you integrate from t = -inf to t = inf, the only non-zero component of the function x(t)delta(t-5) occurs at t=5, and is given by the value x(5). This video might also help: "How to Understand the Delta Impulse Function" th-cam.com/video/xxGcI9WVoCY/w-d-xo.html
Glad you found it useful. You might like to check out the other videos on the channel too. I try to give physical explanations of a wide range of the basic fundamental mathematical aspects of Signals and Systems.
Just to clarify: A function is neither stable nor unstable. Systems and filters are stable/unstable. A system or filter with an impulse response that is a delta function, has finite energy (since the delta function has finite energy), and is therefore stable.
Hi I think you make a mistake in the video. At first you say the delta function has an infinite height, and then later on you say it has a height of 1...
Well, yes, but sort of not really. It's common to say that a delta function has a "height", even though technically it's really the area, because it's not possible to draw something with infinite height. So in practice we draw the delta function using a vertical arrow with a finite height that equals the area of the true delta function. So technically I should have said that "the arrow-representation of the delta function has a height of 1", but that's a bit of a mouthful. It's what we call a "slight abuse of notation". It's done because it makes sense intuitively. For example, if a delta function is multiplied by 2, then it helps to show that graphically, by drawing an arrow with a "height" of 2 (even though it's really the infinitesimally narrow area that is multiplied by 2).
Best channel on signal and systems I have seen, create content with clear simple explanations.
Thanks for your nice comment. I'm glad you've found the videos helpful.
Thank you. The delta function showed up in my strength of materials course and I had no idea what was going on. This makes a lot of sense.
That's great. This video might also help: "How to Understand the Delta Impulse Function" th-cam.com/video/xxGcI9WVoCY/w-d-xo.html
Best explanation and demonstration of the delta function I have seen! Thank you and keep up the amazing work!
Thanks for your nice comment. Glad you liked it.
That delta(t-T) repeatedly confused me, but Iain shows that it's the variable t that (as I think of it) leads and moves over time (the variability based in time) to the constant at set moment T. Then, the delta "strikes" at time t=T.
appreciate such a great video！
Glad you liked it!
Nicely explained. Thank you sir
Glad you liked it
Good explanation, thank you
great work sir
Glad you liked it.
incredibly helpful
Glad it helped!
All the content you are provide was just amazing but i have doubt is that you said that amplitude is infinity at t=0 but also you said that at t=0 height is 1 why?
Ah, good point. Technically, the delta function has an infinite amplitude, and infinitesimally narrow width. The important thing is the area that results from multiplying the amplitude with the width. We draw delta functions with a vertical arrow, and often we draw the height of the arrow to indicate the area. Eg. a delta function with area =1 would be drawn half the height of a delta function with area =2. So sometimes people refer to the "height" of the delta function, when they actually mean the "area".
@@iain_explains what will be the area if -2 is multiplied with delta(t)?
Thank you. A really intuitive approach!
Glad it was helpful!
thank you sir, it helps a lot...
Shouldn't the integral go from 0 to plus infinity?
I'm not sure why you think this. I'm just showing some examples, so I could choose to integrate over any range I like. Maybe you are thinking that "time" can only be positive? If so, then it's important to understand that the "zero" time in any graph is simply a reference time, so negative time simply means the time before the reference time. And also it's important to understand that I could have used any symbol for the "x-axis" - it didn't need to be "t", and it didn't need to represent "time". It is just the variable for the function. The properties of delta functions hold for any "x-axis" variable that takes continuous values (eg. distance, height, length, temperature, acceleration, ... whatever)
That was very good!
Thank you for the explanation sir!
You're welcome. I'm glad you liked it.
Dr Peyam on TH-cam says that the Dirac delta function is a distribution and not a function. What is a distribution?🤔
I'm not sure what that refers to. Usually the term "distribution" is used in the context of random variables.
It's Nice, Thank you sir
Got it. Thanks.
What I do not get is when the variable t is not 5, the function is equal to 0. In the last example, how do they add up to Ax(5)? When t is larger than 5, the function takes on the value of zero. So if we multiply it with x(t=5), isn't it equal to 0?
For all values of t that do not equal 5, the function x(t)delta(t-5) = 0. So when you integrate from t = -inf to t = inf, the only non-zero component of the function x(t)delta(t-5) occurs at t=5, and is given by the value x(5). This video might also help: "How to Understand the Delta Impulse Function" th-cam.com/video/xxGcI9WVoCY/w-d-xo.html
Thanks for offering us an expedited way to understand what a delta function is :)
Glad you found it useful. You might like to check out the other videos on the channel too. I try to give physical explanations of a wide range of the basic fundamental mathematical aspects of Signals and Systems.
Really awesome video
Thanks. Glad you liked it.
thank you
You're welcome
Good job
Thanks
Got it sir, thanks!
Great!
Thanks, I had got this graphically, but now mathematically as well.
Glad it was helpful.
Hi. I like the simplicity of your explanation. New subscriber. I would like to know if a delta function it's stable
Just to clarify: A function is neither stable nor unstable. Systems and filters are stable/unstable. A system or filter with an impulse response that is a delta function, has finite energy (since the delta function has finite energy), and is therefore stable.
Amazing
The best!
That's pretty awesome!
Glad you think so!
neatt thank you
Glad you found it useful.
Hi I think you make a mistake in the video. At first you say the delta function has an infinite height, and then later on you say it has a height of 1...
Well, yes, but sort of not really. It's common to say that a delta function has a "height", even though technically it's really the area, because it's not possible to draw something with infinite height. So in practice we draw the delta function using a vertical arrow with a finite height that equals the area of the true delta function. So technically I should have said that "the arrow-representation of the delta function has a height of 1", but that's a bit of a mouthful. It's what we call a "slight abuse of notation". It's done because it makes sense intuitively. For example, if a delta function is multiplied by 2, then it helps to show that graphically, by drawing an arrow with a "height" of 2 (even though it's really the infinitesimally narrow area that is multiplied by 2).
69th like. 🙂Niceee