Time domain - tutorial 7: system properties

[@andrewlebedev7749]

Man, this stuff needs to go viral! Really helped me with grasping the foundations! One remark- the example starting around 16 minute mark got me a little confused with the technical explanations of change of variables, until I realized that if you substitute upper limit of integration (or lower one, obviously) into the equations 1 and 2, without getting rid of Tau, you end up with exact same result in both cases. Maybe some of you would find this a bit more intuitive. Great job overall though, Iman! Hopefully you can cover some more of Elec 260 (Continuous-Time Signals) stuff before the end of fall. I truly believe your work is the ultimate ticket to passing this course!

[@Kuchdelan]

Thank you very much for your positive feedback. Please tell your friends about this channel. I am really working hard to make all tutorials for ELEC 260 before the end of this term.

[@Awesomer5696]

I just wanted to thank you, I had a terrible teacher and was thrust into fourier and laplace with no prior understanding of signal processing or anything, and these videos have really saved me.

[@Kuchdelan]

such a great pleasure to help you understand the topic ;)

[@Ed-xy5kn]

The most underrated tutorial video ever on KZbin. GOAT!

[@Kuchdelan]

The kindest comment ever! GOAT :)

[@ozzyfromspace]

“You see, your friend is completely crazy and not normal” 😂😂😭 I felt that Iman, your lectures are the best!

[@Kuchdelan]

I'm so glad you liked my lectures. Cheers!

[@pursuantspy1557]

You rock I spent an hr trying to figure this out and this video explained it in 2 minutes

[@Kuchdelan]

Pleasure to help.

[@ravireddy4368]

Your video cleared the doubts I had. Thanks a lot. Keep up the good work.

[@Kuchdelan]

Pleasure to help, Ravi!

[@dallasdominguez2224]

Excellent video my man. Great mathematical examples as well as conceptual examples!

[@Kuchdelan]

Much appreciated!

[@vinitsrivastava9714]

Concept of linearity explained is really awesome. Human interactions.

[@Kuchdelan]

Thanks my friend, happy that you like it ;)

[@ziyuewu9528]

most helpful video on youtube. thumbs up for u man ; )

[@Kuchdelan]

Cheers!

[@colemanjackson516]

I have watched a few of your videos and your explanations are fantastic. Thank you!

[@Kuchdelan]

thanks coleman, you are fantastic too ;)

[@nnakova8775]

Thanks to the comment from @Andrew Lebedev and a lil bit of more thinking included, I finally understood the example at 15:40. It doesn't matter if we restrict the integration through the upper limit or the shift of the function. 1) The upper limit t restricts the integration till the time t, but the function also additionally has -T, thus one more restriction in time. 2) The upper limit is t-T, but -T now is directly in the upper limit and not in the function,. Wow finally understood it. :D

[@Kuchdelan]

Sorry if my explanation was not clear enough! I did my best to simplify it. I am happy that you finally got it. Best!

[@devlyndorfer4931]

10/10 video dude, that helped so much.

[@Kuchdelan]

Thanks a lot.

[@sasankgs9339]

bruh imma pass my midterm exam because of you

[@Kuchdelan]

you passed because you studied hard. Cheers!

[@Andrei-ds8qv]

Very nice, usefull and well explained videos!! With time you will gain more and more views!! you are doing a great job man! thanks!

[@automechanicalengineering3750]

These videos are brilliant!!!

[@Kuchdelan]

Thank you very much!

[@Sweets-o0o]

thank you very muxh, it's now when I understand the learning of some mathematic principal

[@Kuchdelan]

thanks ;)

[@56ur4]

Perfect tutorial man, thank you so much

[@Kuchdelan]

Glad it helped!

[@hussainmayouf5835]

thank you so much because i understood everything in this tutorial

[@Kuchdelan]

thanks for watching :)

[@tasnimhasan3129]

you"re awesome bro!!!hope to get more videos like this..

[@Kuchdelan]

thanks a lot. cheers!

[@tasnimhasan3129]

you can add laplace transform tutorial..more relevant examples can be helpful..

[@Kuchdelan]

sure.

[@gabrielmenezes1361]

hey, quick question: if in the minute 15:40 i had y(t) = cos(t+2) * x(t-2); how would i have to put that T to check if it was time invariant?

[@Hellenic_Empire]

Late, but replace t itself by t - T

[@ab-ie2um]

0:12 memoryless 3:27 causality 6:05 stability 10:17 invertible 12:24 time invariant 17:48 linear

[@Kuchdelan]

Thanks for your kind words! I will make more videos for sure

[@noursalm2580]

really thank you , you helped me to understand it

[@Kuchdelan]

thank you!

[@chingchaolan534]

hello, iman, it is an excellent work, I've learned a lot, thanks. One question, at 14:26, when you talk about the time-invariant, for the first example, you said"shift input by T ", but in the example, why you consider 2*t as the input and shift it by T, however, I think the input should be t anyway? The 2*t belongs to the system property.

[@Kuchdelan]

Thank you very much for your positive feedback. Regarding your question, please note the input is not t but x. The input, i.e. x, is a function of t. Hope this helps!

[@chingchaolan534]

@@Kuchdelan got it! thanks again!

[@Kuchdelan]

no problem!

[@vanibh93]

brilliant work... very helpful...

[@Kuchdelan]

thanks a lot!

[@karthikmurthy2511]

Great video.

[@Kuchdelan]

Thanks for the visit!

[@dr.duraidyehya8768]

Dude This Video Helped Me.

[@Kuchdelan]

Thanks a lot, dude!

[@kibibu]

Brilliant stuff!

[@Kuchdelan]

Thank you very much.

[@bader2017]

At invertible property, the system shouldn't be one-to-one and onto at the same time?

[@teerathkumar9842]

At 5:20, in y(t) = cos(t+1)*x(t), if we put t=89, what you say about causality?

[@Kuchdelan]

I would say it is causal :)

[@seventyfive7597]

I'm not from control studies, but something troubles me. At 7:30 you show 3 examples, by your definition all are stable, yet you say the last two are not. Say the 2nd is e^x, while it tends to infinity, we don't really care, as for a bounded input |x| < M, we have a bounded output 0 < f(x)

[@seventyfive7597]

And you drop the need for a function to be surjective in order to be invertible. Look, I got it now, I should not expect exact science approach here, and I'll stop nitpicking, but man, these are not small nitpicks, you "lighten up" definitions and it confuses more than it helps in my eyes.

[@jawadasif8130]

great explanation even for non having background

[@Kuchdelan]

Glad it was helpful!

[@ionni73]

Hi Iman. Thanks for these excellent playlist (signal processing 101). The simple function examples are what makes them really understandable. You have an excellent didactic! Thanks again. One question: at 21:22 you sum the functions y1and y2. I would have expected the result to be y3= (ax1+bx2)+c (where c is a constant =a+b). Did I missunderstood your example? Thanks

[@Kuchdelan]

Hi Jonathan. Thank you very much for your positive feedback. To check if the system is linear, first you need to apply a linear of combination of x1 and x2 (i.e. ax1+bx2) to the system. This means you should replace the input by ax1+bx2. By doing that you will get: y3=(ax1+bx2)+1. Please note that I am just replacing x in this system y=x+1 by ax1+bx2. Then, you need to create ay1+by2 which is a(x1+1)+b(x2+1) = ax1+bx2+a+b. Finally, you need to compare y3 with ay1+by2. If they are equal, the system is linear. It is clear that the constant terms are different. Therefore, the system is not linear. I hope this explanation helps.

[@ionni73]

ah, got it: inserting x1 and x2 in the original formula --> y(x1,x2)= (ax1+bx2)+1; this is different to the linear combination y3=y1+y2=(ax1+a)+(bx2+b). Thanks

[@abbasbookwala]

can you please review the first example of Time Invariant system y(t)=x(2t) as I feel the shifting for x(2t) by T should be x(2(t-T)) and not x(2t-T)..It may have brought us to wrong conclusion..

[@vinitsrivastava9714]

Seeing you between videos to explain sonething is much more conducive.

[@Kuchdelan]

Cheers!

[@mikeviala3579]

Thanks a lot for the video Iman. Very Helpful. I am confused about one thing though. At 17:45 in the last example for TI, you switch the variable name of K with Tau. I understand that you can call the variable anything you like, but you've already defined Tau's relationship with K, so I'm confused how you can drop the relationship to make the equations equal.

[@Kuchdelan]

Thank you Mike for your positive feedback and sorry if I made you confused. If the last step is confusing, you can simply skip it. Basically, the integral that I have at 17:32 is equal to (2). The integral of x(t) dt from "a" to "b" is exactly equal to the integral of x(k) dk from "a" to "b". The integral variable is just a name. Hope my explanation helps.

[@ShampooWow]

Nice video! I like it

[@Kuchdelan]

Thank you.

[@user-pf3vz3rd9h]

Hi Iman, I really hope you answer my question. At 5.59 you denoted to+1 as a future value, but we had established t+1 means a delayed signal, isnt it supposed to be moved to the left?

[@chawnneal3103]

me: **laughs** my sister: why are you laughing, shouldn't you be studying? me: First let me intuitively explain what a linear system means and why it's valuable...

[@Kuchdelan]

Hahaa! Glad you had fun :)

[@alphasatari]

Hey Iman, I’ve a question. Will a system still be a stable if it produces bounded output for unbounded input?

[@Kuchdelan]

Yes but if you can find JUST ONE bounded input which produces unbounded output the system is not stable.

[@alphasatari]

iman Thank you! You’re awesome.

[@abdelrhmanyousri5915]

fantastic !

[@rafidnabil5894]

u r genius

[@Kuchdelan]

u r kind ;)

[@dipiroy5875]

in the first example of causality, can i know why u let t=-1 ?? if we let t=1... it would be y at 1 is dependent on x at -1 ,which would be causal ... but letting t=-1 made it non causal !! (same in the last exaple of causality too)

[@Kuchdelan]

Finding JUST ONE example that doesn't satisfy the definition of causality would be enough to say the system is not casual. The system is either causal for all ts or not. Hope this explanation helps.

[@dipiroy5875]

iman sir thank you :-)

[@Kuchdelan]

very welcome!

[@mjz-e9i]

Thanks very much！

[@Kuchdelan]

You are very welcome my friend ;)

[@Andrei-ds8qv]

your friend is basically crazy Hahahaa :D

[@Kuchdelan]

:)

[@waleedalsharif1183]

happy new 2018 year my friend...

[@Kuchdelan]

Happy 2018, my friend. All the best in the new year ;)

[@waleedalsharif1183]

iman can i ask you a question when you thinking about change your life and your objective from all life when i start Another one can i give me your number or any chatting program to talk personally

[@waleedalsharif1183]

I’m from Saudi Arabia and half of me Egyptian i need to replied to me

[@waleedalsharif1183]

Finally thanks for you to advice me

[@Kuchdelan]

Hey Waleed. Thanks for your personal interest to talk to me but I am still trying to figure out the main objectives of the life for myself! So, I am not really a good person to answer this question ;)

[@thirteenlao443]

Happy 2019, everything is ok

[@Kuchdelan]

Happy new year my friend!

[@Mazz_1.0]

you are awesome :)

[@michelebianchi7861]

great but those x's look like n's

[@Kuchdelan]

Lol! Sorry for the confusion