Electrical Engineering: Ch 19: Fourier Transform (9 of 45) Conv. from Fourier Series to Transform

In this video I will explain the relationship between the Fourier series and Fourier transform with respect to the number of pulses.

Next video in this series can be seen at:

[eddie]

Thank you for the great lectures. I have a question.
How come the pulse width is 1?
It goes from -1 to 1, so I believe it should be 2 instead.

[terziwh]

Thank you very much sir for covering this very important topic. I have searched the whole youtube and nowhere was a channel found which covered this topic in this depth as you are doing. Thank you very much and hopping that soon this series will be finished. My, and many others', whole semester depends on the lectures on fourier transform and the completed series of laplace transform...

[khaileng]

Hi, Mr.michel, please continue this series

[RodNaugler]

I have a question. For the first series, you describe the pulse width as being tau=1, and all the pulses except the one on the 0 axis are, indeed, 1. If the first pulse actually runs from 0 - 1, with it's center at 0.5, then the period, T, is 2 as the pulses start at 0, 2, 4, 6, etc. and the centers are at 0.5, 2.5, 4.5, 6.5, etc. Is the confusion I am having stemming from the way the function was drawn? In other words, the spacing between -1 and 1, on the graph, is equal to the spacing between 1 and 2, but it should be double?

[farazg]

was esTruggling with a similar problem last nighT. thankS verY mucH for your contributioN siR, you are of greaT h3lp to mE and manY otHer esTudentZ!!!!

[TechSouls-wnjc]

amzing explantion of conversion process from Fourier series to FT

[Muck-qyoo]

But how is the pulse width related to the frequency? If you listen to the fundamental of a rectangular wave at 432 Hz it is the same as for a sine wave at this frequency.

[christopherkhill]

Michael, can you explain the pulse at t=0 ranging from -1 to +1? Everything else is clear enough, but the double pulse width has me puzzled. Thanks.

[ayoobamer]

thank you sir about these courses please continue

[chanwoo]

Thanks for your video. I have gained understanding of mathematical foundation of what the fourier transform is! I also want to know something else in fourier transform. I have been trying to find an easy, SOLID derivation of conversion from fourier series to fourier transform. I have looked into many sources but still could not find the one that clearly shows this derivation process in step-by-step manner with at least a brief explanation on how each step is performed. If you do happen to know it, it would be fantastic to let me know~

[shafiq]

Hi! Your lectures have been helpful! Will you be uploading the rest of the videos?

[varunnagpal]

The top graph seems incorrect for T=2. The centre of first pulse to right should be marked at t=2 and not t=2.5

[DerekDavidLockhart]

So if the central pulse is supposed to be 1 unit wide. should it be 0 to 1 and the pulses before 0 moved up?

[ajj]

i do not understand this when i try to look at the fourier series equation and the period T does towards infinity. f(t)= a0 + sum from n=0 to infinity (An cos(nwt) + Bn sin (nwt) )
a0 = 1/T * integral from 0-T of f(t)
An = 2/T * integral from 0-T of f(t)*cos(nwt)
Bn = 2/T * integral from 0-T of f(t)*sin(nwt)

As limit of T approaches infinity
you get a very small number times an integral from 0 to a very large number. how does that become the Fourier transform

[myonlynick]

0:21, i think that based on the drawing the Pulse width is 2, not 1, because 1-(-1)=2. I suppose the author might fix that slip up in the future :P

[zacharythatcher]

I did not realize that the graph on the right is the amplitude spectrum without a phase. Now that I see that, I can see what this is saying.

[curtpiazza]

Cool! 😂
Is is just my imagination?....or does this concept of amplitude spectrum applicable to spectroscopy in Orgo Chem? 😮

[mamdouhegy]

How the pulse width is 1؟ and it is from -1 to +1 ؟

[ankur]

it is always that for a sinwt and coswt you use delta function formulae and in othercase not why