Trigonometric Fourier Series (Example 1)

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  • เผยแพร่เมื่อ 7 ธ.ค. 2024

ความคิดเห็น • 183

  • @theronwebber1024
    @theronwebber1024 3 หลายเดือนก่อน +9

    These videos are saving my butt right now. This is by far the best series on applied Fourier mathematics that I've found on the Internet. The OpenMIT videos by Professor Oppenheim who wrote the book on signals doesn't even hold a candle to how easily you're able to describe these topics to the layman student. Thank you for this pot of gold! ❤🎓

  • @AquaLifebygauravkumar
    @AquaLifebygauravkumar 5 ปีที่แล้ว +32

    Sir your explantion us better than my collage professor they only rush in class they dont teach the basic one and this lead more difficut to understand the topic thnxx sir for creating this channel

  • @mustafanaser9789
    @mustafanaser9789 3 ปีที่แล้ว +39

    Thanks from Germany! :)

  • @mainkordormawblei
    @mainkordormawblei 3 ปีที่แล้ว +48

    integration of cos(zt) w.r.t dt is 1/z*sin(zt). which is way simpler than changing the limits

    • @Tammy-mq9ng
      @Tammy-mq9ng 2 หลายเดือนก่อน +1

      so in the end you substitute z with n*pi/2, is that what you mean?

    • @shubhamtiwari9611
      @shubhamtiwari9611 2 หลายเดือนก่อน

      ​@@Tammy-mq9ngyes exactly

  • @m.hareni11stdbio-comp95
    @m.hareni11stdbio-comp95 4 ปีที่แล้ว +17

    Omg what a lecture Sir , your lectures are beyond perfection... it's a gift for every engineering student . Thank you from the bottom of my heart . 🙏🙏🙏👌👌

  • @cyanide5188
    @cyanide5188 6 ปีที่แล้ว +501

    This makes me wanna leave engineering

    • @potatoguy8390
      @potatoguy8390 6 ปีที่แล้ว +26

      why? its one of those beautiful creation that mankind
      ever made

    • @KabooM1067
      @KabooM1067 6 ปีที่แล้ว +15

      Probably not a bad choice... Engineers are paid horribly nowadays (depending on where you live though).

    • @KabooM1067
      @KabooM1067 6 ปีที่แล้ว +11

      Tbh though he kinda overcomplicates it a bit here. When finding "an" there was no need to explain when it's 1,5,9 or 3,7,11 etc... Just by substitution into a calculator you can find if it's positive or negative.

    • @johanl7477
      @johanl7477 5 ปีที่แล้ว +28

      You just increased my salary thanks kid

    • @sketch1625
      @sketch1625 5 ปีที่แล้ว +14

      @@johanl7477 what a confident young man. You get a cookie for your hard work

  • @SillyLittleMe
    @SillyLittleMe 4 ปีที่แล้ว +16

    Very detailed and essy to understand way of explanation. It also helped to brush up my old concepts of trigonometry as well. Fabulous series to say the least from the best teacher

  • @gokenriba08
    @gokenriba08 6 ปีที่แล้ว +21

    U are an angle n savior sent by God..ty so much..ur videos are really helpful.. because of u I could clear my Digital well.. looking forward for more videos 😊

    • @calebadobah641
      @calebadobah641 ปีที่แล้ว +1

      Yhhh he is best theta ever😂

  • @mohammedalfaifi8165
    @mohammedalfaifi8165 5 ปีที่แล้ว +4

    Final Expression:
    x(t) = (4/pi) * sigma { [ ( [-1]^[n+1] ) / (2n-1) ] * cos( [2n-1] / 2) * pi * t }

  • @andreasefstathiou9357
    @andreasefstathiou9357 4 ปีที่แล้ว +7

    This is so damn easy at last, high school math teachers suck so bad that trigonometry was the problem following all along college. Thank you for showing the concepts in a so simple way!

  • @saurabhkumarjha4996
    @saurabhkumarjha4996 6 ปีที่แล้ว +13

    at 17:54, before you are converting sin(3n pi / 2) to -sinn pi / 2 you made a mistake in putting odd value 1.....check it

  • @MatheusSilva-dragon
    @MatheusSilva-dragon 4 ปีที่แล้ว +12

    Phew! That was long, but really productive!
    Thanks a lot! I've learned a lot!

  • @adeebabdultaher9721
    @adeebabdultaher9721 3 ปีที่แล้ว +12

    Sir, why did we have to change the integrating variable to theta from "t", we could've proceeded directly and arrive at the same result. at 8:12

    • @ahmetpehlivan3698
      @ahmetpehlivan3698 2 ปีที่แล้ว

      if you find out, can you please tell the reason ?

    • @sahithipattem6151
      @sahithipattem6151 2 ปีที่แล้ว

      @@ahmetpehlivan3698 just substitute corresponding values

    • @anushakommu5177
      @anushakommu5177 2 ปีที่แล้ว

      The solving this integration will be simple if we are substituting as t

  • @loreoyedele4468
    @loreoyedele4468 3 ปีที่แล้ว +5

    From the bottom of my heart thank you sir!!!!

  • @subhadeepgupta571
    @subhadeepgupta571 7 ปีที่แล้ว +4

    very good channel for electronics

  • @antonsonj4995
    @antonsonj4995 3 ปีที่แล้ว +7

    Thanks from a current IIT Electrical Engineering Student! You teach so awesome!!! Better than all our profs! Thank you sir ☺

    • @niteshchaudhary8052
      @niteshchaudhary8052 3 ปีที่แล้ว

      hi bhaiya, actually m not able to understand signals and systems , please bhaiya can u pls pls help me in my mid sem ,

    • @v_stechgamer7725
      @v_stechgamer7725 2 ปีที่แล้ว

      Plz can u help.me to understand signal.and system urgent bro

    • @alien77333
      @alien77333 5 หลายเดือนก่อน

      @@v_stechgamer7725 help kiya kya?

  • @xXMaDGaMeR
    @xXMaDGaMeR 10 หลายเดือนก่อน +1

    there seems to be a big need for good understanding of trigonometry, any recommendation of series / books / lectures to get better understanding of how you switch around and manipulate the sins / cos, everything was very excellently explained, but the trig was a bit confusing.

  • @vakhariyajay2224
    @vakhariyajay2224 2 ปีที่แล้ว +1

    Thank you very much. You are a genius. 👍👍👌👌🙏🙏🔝🔝

  • @renukaverma5752
    @renukaverma5752 5 ปีที่แล้ว +6

    Thank u so much sir ...ur way of explaination is very good 😊

  • @justlikeyourfathersaid
    @justlikeyourfathersaid 25 วันที่ผ่านมา +1

    isnt the equation: (-sin(n*pi*3/2) = sin (n*pi/2) / ∀ n ∈ ℕ )? and we know n ∈ ℕ since its a Σ from 1 to ∞
    So the equation answer should be: (4/(n*pi))*sin(n*pi/2) for every case

  • @ashokbanjara6323
    @ashokbanjara6323 6 ปีที่แล้ว +3

    Explained very well Sir good job

  • @Bhaskar5554
    @Bhaskar5554 5 ปีที่แล้ว +3

    It is really good explanation ....sir ......plzzzz upload more video .....for gate ....

  • @ronniewhyrick
    @ronniewhyrick 6 ปีที่แล้ว +6

    i don't understand how you know that when n=even that sin(3*pi*n/2) that you know it's in the first quadrant literally plug any value in for 'n' and you'll see that's not the case. n =2 makes sin(3*pi) -- not in the first quadrant, wtf.

    • @Hiyori___
      @Hiyori___ 3 ปีที่แล้ว +1

      he does not say that sin(3*pi*n/2) is in the first quadrant. He says that if you add something to sin(n*pi) which is always 360, you end up in the first quadrant where sin values are positive. From that he gets a positive sin(n*pi/2) equivalent to sin(3*pi*n/2).
      In fact if n=2:
      sin(3*pi*n/2) becomes sin(3*pi)=sin(180°)
      sin(n*pi/2) becomes sin(pi)=sin(180°)

  • @theoracle4224
    @theoracle4224 3 ปีที่แล้ว +2

    Thank you form India

  • @parush5381
    @parush5381 ปีที่แล้ว

    bestest explaination god bless sir😊😊😊😊

  • @humzaali7583
    @humzaali7583 2 ปีที่แล้ว +1

    why does sin changes to cosine when we plus or minus it from 90 or 270 degree ? 17:03

  • @nitinkamra8972
    @nitinkamra8972 5 ปีที่แล้ว +2

    wow amazing...sir thanku soo much.

  • @stylingandfitnessingwithty2713
    @stylingandfitnessingwithty2713 4 ปีที่แล้ว +7

    16:54 why did that come to sinnπ/2

    • @Hiyori___
      @Hiyori___ 3 ปีที่แล้ว +1

      because if n is even (2,4,6...) sin(nπ) is always "equal" to 360° where value of sine is 0. So the nπ goes away because it always provide a value of sine equal to 0.

  • @mohitzen
    @mohitzen 2 ปีที่แล้ว

    I'd have stucked after the case when n=odd. Thanks.

  • @derangulasaikumar64
    @derangulasaikumar64 3 ปีที่แล้ว +1

    Good job brother

  • @saketsamrat5038
    @saketsamrat5038 3 ปีที่แล้ว

    Happy Teacher's day sir

  • @jaanvi25
    @jaanvi25 4 ปีที่แล้ว +1

    Signal is unsymmetrical about x axis. How come a0 is 0 then? Please explain

  • @sushantshukla6673
    @sushantshukla6673 6 ปีที่แล้ว +1

    Good and detailed explanation

  • @Hiyori___
    @Hiyori___ 3 ปีที่แล้ว +2

    that trigonometry ratios explanation was very helpful

  • @sahabtareq
    @sahabtareq 2 ปีที่แล้ว +13

    idk why i picked engineering tbh

    • @khoanguyen-ej9md
      @khoanguyen-ej9md 7 หลายเดือนก่อน +1

      Me too, i both love and hate this major 😢

    • @Ssathudharu
      @Ssathudharu 3 หลายเดือนก่อน

      ​@@khoanguyen-ej9md me 2

  • @auhontussh
    @auhontussh ปีที่แล้ว +2

    Actually this could be solved in much smaller way but i think he followed the general way

  • @jushas9276
    @jushas9276 6 ปีที่แล้ว +2

    what a big problem it is!
    the lecture is really good

  • @mohanvamsi1180
    @mohanvamsi1180 5 ปีที่แล้ว +1

    This is making a lot of difference from what I just learned from my textbook also see the book B.P LATHI so that you can make sure you make the video in the perspective of this textbook.

  • @thetruth9923
    @thetruth9923 6 ปีที่แล้ว +1

    hey first of all thanks for the video... can u show how to flip the signal on Y axis by pictorial representation...i m stuck at the flipping ...not understanding the flipping thing..

  • @sreejithsuresh2543
    @sreejithsuresh2543 ปีที่แล้ว

    Sir can we also take the half wave symmetry of the signal as it is not even nor odd.

  • @paappu-gr3up
    @paappu-gr3up 8 วันที่ผ่านมา +1

    Why this is so complicated......😢
    Please explain in easy way

  • @achyuthrahul9854
    @achyuthrahul9854 3 หลายเดือนก่อน +1

    Shit goes hard🔥🔥

  • @armanharis6594
    @armanharis6594 5 ปีที่แล้ว

    Kl exm h r aj pta chla k ye sb pdhna h...

  • @jayeshkulkarni226
    @jayeshkulkarni226 4 ปีที่แล้ว +5

    Could have solved in much simple way

  • @sagelioneldsouza8230
    @sagelioneldsouza8230 7 ปีที่แล้ว +3

    Dear sir, In m3 degree, according to what I've learned, whenever the function is even, only bn gets cancelled, how does the average time of every cycle, determines a0?

    • @wilbowednesday1417
      @wilbowednesday1417 7 ปีที่แล้ว +1

      The amplitude (1) and time duration ( 2 seconds) of the signal below and above the x-axis are equal so the average is 0. You can calculate the D.C coefficient but it will only confirm your inspection that Ao = 0

    • @sagelioneldsouza8230
      @sagelioneldsouza8230 7 ปีที่แล้ว

      Wilbo Wednesday ooh.. So if suppose A0 is equal to average time, what are an and bn?.. I know its a vague question but asking just to clarify
      ``\_('u') _/``

    • @anishkumar2074
      @anishkumar2074 7 ปีที่แล้ว

      even signal consists of Ao &An and Bn=0, so this statement is contradicting witht the above statement .....and we know that cosine signal have both Ao and An terms in it(Wilbo Wednesday ) and cosine signal is similar to the above mentioned signal in a some way

    • @neekuenduku
      @neekuenduku 6 ปีที่แล้ว

      The area under the curve x(t) for a particular time period represents the average which is nothing but dc value of wave

  • @JL-bc6zl
    @JL-bc6zl 3 ปีที่แล้ว +1

    if we use sin(npi/2)=(-1^n) and sin (3npi/2)=(-1^n) for when n is odd, is it ok?

  • @nettrikan6333
    @nettrikan6333 3 ปีที่แล้ว +1

    Thanks from kailasa ....

  • @hari8568
    @hari8568 6 ปีที่แล้ว

    Sir this function is both even and odd? Only fx=0 is a function which satisfies this condition right

  • @SandeepKumar-up9bp
    @SandeepKumar-up9bp 6 ปีที่แล้ว +4

    sir could u plz tell me y we r taken 2 types of odd numbers i.e n=1,5,9,13 and another one is n=3,7,11,15 ?

    • @zaidizawawi5033
      @zaidizawawi5033 3 ปีที่แล้ว

      Based on even and odd

    • @engineer3961
      @engineer3961 2 ปีที่แล้ว +1

      for n = 1,5,9.... ----> sin (pi/2)n = +1
      for n = 3,7,11... ----> sin (pi/2)n = -1

  • @roushansingh9936
    @roushansingh9936 2 ปีที่แล้ว

    LOved tHIS!!

  • @muhammadibnwahid6405
    @muhammadibnwahid6405 5 ปีที่แล้ว

    Why didn't you put values of cosines in the final expression? cos of pi/2 is 0 and other terms of cosines are also zero in the final expression.

  • @sachinjainwar8293
    @sachinjainwar8293 ปีที่แล้ว

    sir i need your notes . please tel me how can i get ? very needy

  • @ramasaleh5702
    @ramasaleh5702 ปีที่แล้ว

    how did u find that To=4sec & other...

  • @ranjansrivastava4455
    @ranjansrivastava4455 6 ปีที่แล้ว +2

    thanks very informative.

  • @haribabureddy1173
    @haribabureddy1173 7 ปีที่แล้ว +2

    Thank u so much upload videos as early as possible

  • @جناتالنعيم-خ5ع
    @جناتالنعيم-خ5ع 6 ปีที่แล้ว +2

    sir how can you take common
    2/npi it represents angle not value

    • @sowjanyadevi6132
      @sowjanyadevi6132 5 ปีที่แล้ว

      No . He did that problem in another method ( substitution) its correct ans . In anther method without substitute applying direct integration it represents angle

    • @sowjanyadevi6132
      @sowjanyadevi6132 5 ปีที่แล้ว

      In this method 2/ npi represents a value

  • @ahmetkoraysonal5841
    @ahmetkoraysonal5841 5 ปีที่แล้ว +1

    firstly thank you for your courses.I have a question.Can we make a generalization like this?If our function is even, it consists of single harmonics or
    single function consists of double harmonics can we say?

    • @Borz091
      @Borz091 4 ปีที่แล้ว +1

      Might be a little late, but if the function is even, it contains only cosine harmonics, if a function is odd, it contains only sine harmonics

  • @UDYAN_ABHA
    @UDYAN_ABHA 4 ปีที่แล้ว

    Please make such videos on op-amp please please please

  • @krishnenducgec7195
    @krishnenducgec7195 6 ปีที่แล้ว

    Thank you very much for this lecture... but can you say why "sin(3*n*pi/2)=-sin(n*pi/2) for n=odd.???? please give me reply...

    • @easybreezy3913
      @easybreezy3913 5 ปีที่แล้ว +1

      Sin3pi/2=sin(pi+pi/2) which lies in 3rd quadrant (in 3rd quadrant sin is _ve )sin(pi+thetha)=-sin(theta)

  • @samiyainsramkhan8665
    @samiyainsramkhan8665 7 ปีที่แล้ว +1

    didn't got the concept of how a0 became zero plz explain ,how area cancellation made it zero?

    • @aaqibbhat7500
      @aaqibbhat7500 7 ปีที่แล้ว +1

      samiya murtuza a0 is average value and here average value(area under time period) is zero because +ve and -ve cycle will get cancelled

  • @mahjoubahmed1287
    @mahjoubahmed1287 4 ปีที่แล้ว

    Thank you very much

  • @bishalghoshb3412
    @bishalghoshb3412 7 ปีที่แล้ว +2

    Thanx & PLS UPLOAD MORE VIDEO

  • @yash1152
    @yash1152 2 ปีที่แล้ว

    > _"Trigonometric Fourier Series"_
    are there non-trigonometric fourier series too??

  • @fabien20
    @fabien20 2 ปีที่แล้ว +1

    And also different types of functions

  • @urmyakhter7210
    @urmyakhter7210 3 ปีที่แล้ว

    Sir..i want to see practice problm 17.1

  • @-JKalyan-xc1nx
    @-JKalyan-xc1nx 5 ปีที่แล้ว

    Very nice explanation sir super....

  • @PasanJayaweeraYashoda
    @PasanJayaweeraYashoda 4 ปีที่แล้ว +1

    im mr meeseeks! this is me!

  • @P3RYYY
    @P3RYYY 2 ปีที่แล้ว

    In my book time period is from -3 to 3 but the time period is -1 to 3 i am confused

  • @Paradox-ii5ol
    @Paradox-ii5ol 7 ปีที่แล้ว

    Sir please Upload Fourier and Laplace concepts ASAP.....

  • @oggamer2244
    @oggamer2244 6 ปีที่แล้ว

    Shouldn't a(1)=2/pie? Plz help

  • @ninadthite3243
    @ninadthite3243 4 ปีที่แล้ว

    Quadrants explanation for sin(- nπ) 🙌🙌🙌

  • @antoine1407
    @antoine1407 2 ปีที่แล้ว

    is it a rectangular or square signal?

    • @antoine1407
      @antoine1407 2 ปีที่แล้ว

      I guess it's a wave even signal

  • @vijetasarswat9610
    @vijetasarswat9610 7 ปีที่แล้ว +1

    Thanks for the new vedio

  • @vinaychindam880
    @vinaychindam880 2 ปีที่แล้ว

    crystal clear

  • @hycienthemmanuel9857
    @hycienthemmanuel9857 2 หลายเดือนก่อน

    Firstly, the signal is equally symmetrical along the vertical axis, making an=0 as well. Somebody please enlighten me 🤔

  • @victorvas3864
    @victorvas3864 7 ปีที่แล้ว +2

    Hi, thanks a lot for your work ! cos(n*pi*t/2) ----primitive---> 2/(n*pi) * sin(n*pi*t/2) would work too instead of the theta trick no ?

  • @anikatabassumshabiha3351
    @anikatabassumshabiha3351 3 ปีที่แล้ว

    Isn’t the signal is odd signal??
    As x(-t) = x(t)
    Therefore signal is odd..
    How it becomes even? Please let me know.. Thank you..

    • @anubhavrauniyar3192
      @anubhavrauniyar3192 3 ปีที่แล้ว +1

      Put x=-1 and x=1 We Get 1, satisfy property of even signal........Just Think about cosine function in trignometry

    • @mehulkumar1110
      @mehulkumar1110 2 ปีที่แล้ว

      If a function is symmetric along Y - axis (here 'x' i.e signal), then it's an even function which implies that x(-t) = x(t), and if the function is invertly symmetrical, then it's an odd function which implies that x(-t) = -x(t).
      For further clarification, you can check the graph of an even function and an odd function.
      Thank You.

  • @anubhavbansal4003
    @anubhavbansal4003 ปีที่แล้ว

    Your voice is very similar with code with harry

  • @AbdulKader-mj8yl
    @AbdulKader-mj8yl 4 ปีที่แล้ว +3

    I am still confused , what is relation with electrical engineering of those math? I hate communication Engineering part.

    • @MohammadMomin
      @MohammadMomin 4 ปีที่แล้ว

      Bro maths se kab tak bhaagoge

  • @madhavkhindri2817
    @madhavkhindri2817 4 ปีที่แล้ว

    Isn't that cos (nπ/2) = 0 for odd values of n?

    • @hayaalmansoori5905
      @hayaalmansoori5905 3 ปีที่แล้ว

      YESSS, i didnt get it, cuz the answer doesnt make any sense cuz all the cosines gonna be zero

  • @Alex-rv8gw
    @Alex-rv8gw 4 ปีที่แล้ว

    16:18 how can the sin 3npi/2 become sin npi +npi/2 ?????????????????????

    • @iFullofTechHD
      @iFullofTechHD 4 ปีที่แล้ว

      by separating the equation like shown below, they both mean the same thing
      2 (npi) npi 3(npi)
      -- * ------ + ------ = -------
      2 (1) 2 2

  • @SPIDEY_X_GAMING-i3v
    @SPIDEY_X_GAMING-i3v 7 ปีที่แล้ว +2

    Veer Ji waheguru ji ki fateh ji ki fateh

    • @SPIDEY_X_GAMING-i3v
      @SPIDEY_X_GAMING-i3v 7 ปีที่แล้ว

      Sorry veere disturb karn lai

    • @SPIDEY_X_GAMING-i3v
      @SPIDEY_X_GAMING-i3v 7 ปีที่แล้ว

      Mathematics kamm aon ge...veere links send Karn lai thanks ...appa lodd Penn te video jarur dekhage

  • @syedwaleedahmedshah8089
    @syedwaleedahmedshah8089 5 ปีที่แล้ว

    how come an didnt become zero??
    integrals were canceling each other

  • @waleedabdelghany600
    @waleedabdelghany600 3 ปีที่แล้ว

    thank u sir

  • @sagarraj4521
    @sagarraj4521 6 ปีที่แล้ว

    Superb sir

  • @PardeepSingh-wj8lc
    @PardeepSingh-wj8lc 5 ปีที่แล้ว

    Best video

  • @OuttaSyllabus
    @OuttaSyllabus 6 ปีที่แล้ว +5

    HOLY HELL!!! You are an awesome teacher!!! but....... but..... Fourier :\

  • @karanamgopi
    @karanamgopi 5 ปีที่แล้ว

    excellent

  • @bhaskarchakraborty8328
    @bhaskarchakraborty8328 ปีที่แล้ว

    Why you are taking asuffix0 0 we are even symmetry and don't consider ao-0 in even symmetry.

  • @bhargavirobbi1807
    @bhargavirobbi1807 6 ปีที่แล้ว

    Can u please upload lectures for communication systems also?

  • @fabien20
    @fabien20 2 ปีที่แล้ว

    I need domain and range of function

  • @roshansavalapurapu8154
    @roshansavalapurapu8154 ปีที่แล้ว

    superrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

  • @chisomodimmegwa3479
    @chisomodimmegwa3479 5 ปีที่แล้ว +4

    Very complex long method, could have just used the regular limit instead of changing it, now I'm just confused

  • @Unpoplr_opinions
    @Unpoplr_opinions 6 หลายเดือนก่อน

    Neso you almost gave me a heart attack with your explanation but anyways thanks for teaching this course

  • @myselfSrijit
    @myselfSrijit 2 ปีที่แล้ว +1

    you are god

  • @anujaiswal4994
    @anujaiswal4994 7 ปีที่แล้ว

    Plz power amplifier v padha do

  • @nissyvivek87
    @nissyvivek87 3 ปีที่แล้ว

    Watch in 2X to save your time.

  • @iremozgoren742
    @iremozgoren742 11 หลายเดือนก่อน +1

    allahım sen anadili türkçe olup anlamaya çalışanlarında rabbisin
    :(

  • @sujitsharma5158
    @sujitsharma5158 6 ปีที่แล้ว

    what are half range and full range fourier series.....the expression/ formula is a bit different in my book

  • @ramyanaidu7569
    @ramyanaidu7569 4 ปีที่แล้ว

    When will we use integration limits ( t0 - t0+T)