@Neso Academy, sir in previous lectures you have explained how to calculate the Fourier transform of e^(-at).u(t)= 1/(a+jw). Why can't we directly use this in deriving Fourier transform of step signal when you have defined u(t) as e^(-at).u(t) with limit a tending to zero.
EDIT: just watched the next video, skip this comment and watch it. another approach: derivative of u(t)=del(t)... the fourier transform of del func. is equal to 1. since we differentiated the original function the result must be divided by jw ( check properties of FT). so we have 1/jw... then add the FT of dc value which is 1/2 for step function. then using FT of dc value 1/jw + 2pi*1/2*del(t) gives the right answer.
Sir, at 3:57 after performing amplitude shifting by 1 unit , sgn(0)=2 bt it has to be 1 bcz Sgn(t) at t=0 is zero so after amp.shifting by 1 unit it must be equal to 1 . If m wrong plz clear the things ...
Vikas maurya Step signal and Signum function are discontinues at t=0. The value at t=0 is calculated by taking average of amplitude. That’s why 1+sgn(0)=1 and step is 0.5 at t=0. But while dealing with problems we can assume 1+sgn(0)=2 it will not affect our results.
Umm... shouldn't the second step be amplitude scaling... cause we are like scaling the amplitude right? PS: Thanks Neso for everything! You guys are my saviour!
making it converge by multiplying a decaying term to it ( exp() ) just as was suggested for this one, too. However you would have to express the sign function in terms of the unit step to be able to multiply the term to both - the negative and the positive part.
Because Dirichlet conditions are not necessary conditions, but actually sufficient conditions only, i.e., a function satisfying them will definitely be transformed, but all functions capable of being transformed need not be following Dirichlet conditions.
integration in time property will also help since we know the unit impulse func is the differentiation of unit step func. Thanks for your effort. These are great contents.
i love it how you use signum function to find fourier of step, and step function to find fourier of signum...absolutely useless until you derive at least one
![Fourier Transform of sgn(t) & u(t) [Important Shortcut]](http://i.ytimg.com/vi/GCxCHP6QSNM/mqdefault.jpg)
![Fourier Transform of sgn(t) & u(t) [Important Shortcut]](/img/tr.png)
Best channel in entire youTube for learning. Many many thanks for this effort.
why can't I just do integral of e^-jwt (which is 1/jw)
to get unit step 's fourier transform ? @Neso Academy
Thank you for your simple and fluent explanation. Excellent!
@Neso Academy, sir in previous lectures you have explained how to calculate the Fourier transform of e^(-at).u(t)= 1/(a+jw). Why can't we directly use this in deriving Fourier transform of step signal when you have defined u(t) as e^(-at).u(t) with limit a tending to zero.
I think this limit tending is just a approximation ;
so it can't be used to calculate fourier transform directly .
Why can't we take u(t) as e^(-at).u(t) as lim a->infinity and simply use the formula. We would get 1/jw by using this.
Neha Grewal if u take it as infinity then u of t will become zero
So only possible assumption is to take as a tends to zero
Is it clear for u ??????
Neha Grewal it has to be a--->0...Edit it...buddy
@Nesoacademy check this comment and give us the explanation....
@@phanindrareddy4885 if we take a-->0 ans comming 1/jw
See the next video from 9:51, you will get the answer.
wow, one of the best explanation of FT. Great work Sir!
thank you so much, it's really helpful!
thanks for the video that completed a piece of F(Unit Step function) understanding !!!
EDIT: just watched the next video, skip this comment and watch it.
another approach: derivative of u(t)=del(t)... the fourier transform of del func. is equal to 1. since we differentiated the original function the result must be divided by jw ( check properties of FT). so we have 1/jw... then add the FT of dc value which is 1/2 for step function. then using FT of dc value 1/jw + 2pi*1/2*del(t) gives the right answer.
This was useful, thank you
Sir, at 3:57 after performing amplitude shifting by 1 unit , sgn(0)=2 bt it has to be 1 bcz
Sgn(t) at t=0 is zero so after amp.shifting by 1 unit it must be equal to 1 .
If m wrong plz clear the things ...
Vikas maurya Step signal and Signum function are discontinues at t=0. The value at t=0 is calculated by taking average of amplitude. That’s why 1+sgn(0)=1 and step is 0.5 at t=0. But while dealing with problems we can assume 1+sgn(0)=2 it will not affect our results.
Umm... shouldn't the second step be amplitude scaling... cause we are like scaling the amplitude right?
PS: Thanks Neso for everything! You guys are my saviour!
Yes, its a mistake. It should be amplitude scaling.
Sgn(t) is also non converging then how you have taken fourier transform
making it converge by multiplying a decaying term to it ( exp() ) just as was suggested for this one, too. However you would have to express the sign function in terms of the unit step to be able to multiply the term to both - the negative and the positive part.
Because Dirichlet conditions are not necessary conditions, but actually sufficient conditions only, i.e., a function satisfying them will definitely be transformed, but all functions capable of being transformed need not be following Dirichlet conditions.
Helpful, as always.
What is the need of compare with sgn function? Why can't calculate step signal?
THANKYOU SO MUCH , EACH AND EVERY VIDEO HELPED ME ALOT ... :)))))
integration in time property will also help since we know the unit impulse func is the differentiation of unit step func.
Thanks for your effort. These are great contents.
Sir can you please explain the Fourier transform of even and odd function of a signal x(t)???
Ur a genius 🤗
sir pls try to complete syllabus by this month
awesome ty
Awesom sir
sir i will take Lt a->0 e^-at u(t)
then i get 1/jw
but we do in different manner plz judge me sir
sai sumanth see previous lecture of signum
See the next video from 9:51, you will get the answer.
🔥🔥🔥
What will be fourier transform of t/u(t)
Sir why not you done directly F. T. of e^-(at). u(t)
i love it how you use signum function to find fourier of step, and step function to find fourier of signum...absolutely useless until you derive at least one