Time domain - tutorial 6: elementary signals

In this video, we cover two elementary signals, unit step and unit impulse, which will be extensively used in this course. The following materials are covered:
1- definition of unit step and unit impulse functions
2- how to represent any arbitrary signal using unit step over different intervals
3- sifting and equivalence properties of the unit impulse function

Learn Signal Processing 101 in 31 lectures covering time, frequency and Laplace domain in about 8 hours all together:

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References:
[1] Alan V. Oppenheim, Alan S. Willsky, S. Hamid Nawab, Signal & Systems, 2nd Edition, Prentice-Hall, NJ, USA, 1996.
[2] Alan V. Oppenheim, Ronald W. Schafer, Discrete-Time Signal Processing, 3rd Edition, Prentice-Hall, 2009.
[3] Michael D. Adams, Continuous-Time Signals and Systems, University of Victoria, Canada, 2013. Free textbook and lectures (courtesy of Dr. Michael Adams):

[andifin]

first of all thx for your awesome videos, they are very easy to understand without being boring.
in the very end you put the 5 in front of the integral, but you don't use it in your final answer.
As far as i know, your final answer should be something like 5u(t-2)

[tejobhiru]

it feels so amazing to understand it finally..!! thank you so much... i was very confused with all the symbols before watching this video.
now it is crystal clear..!!!!

[cooper]

Thanks a lot Iman, your videos have helped me a lot in understanding basic signal processing. I watched your videos a year ago to help me get through my intro signals and systems course, and I am now re-watching to refresh before a real time dsp lab course this fall.

[horstigerhorstiger]

you are saving me right now! thank you so much for this greatly made tutorial man. Keep up the good work! (thumbs up)

[alonsechan]

Dirac delta function is equal to infinity and not to 1. Because it's integral is equal to 1 and it's width is approaching zero (a width of a single point) it's hight need to be infinity.

Thank you very much for the videos !

[vinitsrivastava]

Joy to watch....Feeling good after understanding. Thank you

[jamesbayode]

How did you arrive at the line equations for the signals in 1:43 and 3:32?

[thirteenlao]

Dear brother, thanks very much, learn more from you, happy every day!

[Alii]

AMAZING MAN
7 years have passed but still very current

[artsiomkaliaha]

this is a brilliant video! double thumb up!

[MaxTube]

Dirac delta function is NOT equal to 1 at t=0: it equals to infinity. But an integral of Dirac delta function is 1. It is very important to understand, but it is shown wrong in this video and some next too.

[moussatouhami]

thanks 4 this clear easy to grasp lecture, my question is at 11:00 u didnt multiply by 5,
another question if u have half circle instead of "(t-2)^2" at 3;20, whats the equation 4 half a circle

[tıbhendese]

I guess you did wrong at 4:27 , impulse function is never 1, it is infinity. The area is 1.
unit impulse function and unit impulse sequence ( DT ) are not same. There is an abstract "impulse to sequence" conversion. It will be helpful if you make a video about CT to DT conversion, about what exactly the process is.
Also, your solutions could be slower. Thanks

[prakashkumarshah]

Hey Iman thanks for this course, it is really very helpful. Btw is there any chance of getting your notes on blackboard slides in any format.

[binshuaiwang]

Hi iman, I like your video very much and I hope you can continue to make it. Besides, at 6:54 in this video, it seems that you forgot the dt in the Integral formula.

[uniqueramya]

Thank you for the awesome explanation. I have a doubt, at 8:10 in the video. we have in 2nd example cos(2t)delta(t-1) with integral.
delta function has t but cos function has 2t. is the 't' in x(t) and delta(t) independent?

[linhnguyen-uexd]

Hi Iman, appreciate the videos, they are of great help!

I'm a bit confuse at 8:00, example 2, as you went a bit too fast, this is my understanding of what happen, and I think it's missing, hope you could provide some clarification:
cos(2t)∆(t-1) = cos(2 * t)∆(t-1) = cos(2 * 1) = cos(2)

[libbyoliver]

At 4:45, how is the function x(t) defined?

[pkl]

can I ask a question iman? in the video at 3:20, when the equation in the below adding together. the value in the origin is 2, not as shown in the triangular which u plot in the begin?

[yogeshghadge]

I didn't got one thing, it's OK that integral us a summation but in the above cases the integrand should be summation of d(t) multiplied by dt. I got that d(t) has value 1 at origin but what about dt???