Intro to Fourier transforms: how to calculate them

[@tavakoliferi1409]

Sir Chris Tisdel. I was looking for information to refresh my memory on Papa Fourier's transforms. Finally I found it. Many thanks Sir, this is one of the best representation and also a beneficial introduction for technicians and also engineers on Fourier transforms. The method and explanation are perfect. great tutor

[@peacewalker991]

This was the most amazing video I have ever watched, explaining how to actually integrate the Function. I got a bit panicky when you missed out the ^2, but you corrected yourself quickly. Amazing tutorial. Will use this is my exploration now.

[@mrigue56]

thanks for all your work Dr. Tisdell, ive come to note your videos are some of the richest in content & have benefited me greatly

[@maxwelledison5436]

Was worth it for the brilliant way way you calculate those integrals, thank you.

[@BentHestad]

So calmly and clearly explained, brilliant! Thank you, Sir!

[@janmpatrika]

first time in years i found youtube usefull. . . thankyou sir . . both the examples you gave , helped me through the section!! its lucky of students around da globe to have social workers like you . !!! haha ty a lot sir !

[@astrofox2409]

Made it so easy. Wow. I cannot express how much I thank you for this video.

[@iijumark]

Hats off to you Sir! You make my Advanced Engineering math look easy! I personally feel that you are among the best tutors out there. And you're " hi, again!", at the beginning of video sounds more like " Eigen". It's so cool!

[@ramzimay9669]

Thank you very much Dr Chris. It is as usually an interesting representation. I have just a simple remark: at the end of the representation when you make the change of the variable z=x+iw/2sqrt(a) the integration becomes on the complex line z=x+iw/2sqrt(a) and via residus theorem we can deduce that the value of the new integral is also equal to sqrt(pi).

[@DrChrisTisdell]

Haha! It is my pleasure and I wish you all the best with your studies.

[@hypatiakovalevskayasklodow9195]

Ah, the pleasure of forwarding to 11:11 and realizing at least I still know how to do some simple partial integration!

[@noahallen9983]

This guy is a life saver.

[@GeminiBeta7]

Shouldn't the third line at 15:31 be w^2/4a^2?

[@bernardlee6271]

get in son, been totally confused in class-this cleared it up cheers fam

[@archiliusfowl3701]

Poto Littlelotte Here j = imaginary number = sq root of -1. j^2 = j * j = -1 So the product (a - jw) (a + jw) = (a^2 - (jw)^2 ) = (a^2 - (-1) * w^2) = a^2 + w^2 : Here ^ stands for power and * is for multiplication. Hope this helps.

[@joeblow4938]

since when doed FT have a 1/sqrt(2pi) in it?

[@fadishahoud3454]

same question.

[@dimitrisr2350]

@@fadishahoud3454 because you want the product of the coefficients in front of the integrals of fourier transform and the inverse to be equal to 1/2π

[@soponyossapong4097]

thank you sir but I'm not sure answer in Ex2 should be( 4a or 4a^2 ) ?

[@maxsalman783]

+Sopon Yossapong I was wondering the same thing. Chris, do you mind enlightening us? :-)

[@abdelhamidelharaki9781]

+Sopon Yossapong you'r right

[@DrChrisTisdell]

+Sopon Yossapong You're right. I forgot the squared, but I've posted a annotation. Thanks!

[@anubis1751]

abdelhamid el haraki

[@calvinjoyce2154]

Nice, succinct explanation... one question: did the 4a, which you corrected to 4a**2, lose the square in subsequent steps?

[@SurendraSahu-sh1rk]

Nice Sir

[@paulbenjamin6597]

its a constant and is taken outside, yes thats a mistake, it should be 4a**2, not 4a.

[@mixas6678]

just logged in to say thank you sir for your videos! very helpful!

[@wellingtonmartins1659]

Obrigado professor! Parabéns Excelente vídeo!

[@husseind1773]

Dear Chris, I need to calculate heart rate variability by using fast Fourier transformation and find total power and High frequency and Low frequency. ex) x=[0.465,0.466,0.470,0.500] How can I do that for above example.

[@fulchy90]

what happens to the i ? why does it disappear?

[@robertsteentjes3870]

Why the square root ?

[@kevinwilfriedngouan6344]

Hi Good work but there is a mistake in FT formula you forgot minus - in the complex

[@nurhazirahrazhan1523]

hi sir...how to determine the limit for the inverse fourier transform?

[@kambuaombo7967]

I'm over blessed with that video!!. Thank you very very much. You explained it very clear and I understand it better. Now I ca handle such problems or even complex ones. Again thank you from the bottom of my heart.

[@chandanadeeksha884]

Hello, I don't quite agree with the correction mentioned in the description saying the "4a" in the final answer of second example needs to be replaced with "4a^2". Didn't we get "4a" only because the second "a" in "4a^2" got cancelled out with the "a" from outside the parenthesis?! What am I missing?

[@tensor131]

Thank you so much for this. Many of the vids on FT do not go into explicit examples and so I am left wondering how does it actually pan out. You have solved this for me - thank you again. Question: in both of your examples the FT of a real function is real, despite having dipped into complex numbers through the definition. Is this the case in general? The first time I saw the definition of FT I thought "that's weird going from a real to complex - how can that be useful" ... so what is the general rule?

[@muhammadhuzaifa1940]

Sir u haven't taken is/2a after derivative

[@aarifhussain3700]

Dr chris I have many questions about functional analysis if you can??????😥😥😥

[@DrChrisTisdell]

I remember! I took me a long time, but I finally have some videos about it.

[@JimboFreshed]

This helped me out a lot, thank you sir!

[@hemjoshi7619]

Great video. Just a question, when you talk about computing the fourier transform, you actually mean to calculate the coefficients, right?

[@studyskilllearn]

Hi Dr can u help me.

[@94ForReal]

Hi, great video. I worked through the same problems on my own after and got the same results by just remembering your process, so I'm getting somewhere. I tried, though, to do the inverse Fourier transform of your second example to see if I could return to the original function. It felt like such a similar process (completing the square and using the standard integral you gave) I thought I was onto a winner, but so much cancelled out and left me with just 1/sqrt(a), not a function of anything.

[@tarshasleak]

hey, I have been watching your videos...I am a major in statistics but I have a mandatory course in PDE this spring. in as much as I am nervous and freaking out, I know with hard work and determination, I will ace this course. I noticed that your videos don't contain problems with initial/boundary conditions especially in the 2nd order PDEs, please kindly make some with conditions...Keep up the good work sir

[@HT-rq5pi]

+tarshasleak i don't think spamming all his videos with this comment is going to get you what you want.

[@libraboya6397]

in formula e^(-iwx) or e^(iwx) ..... i have seen two kinds on net and i m little consfused here... which one to follow

[@LittleLotte5]

also, i need to know why the answer is a2 + w2 , instead of a2 - w2

[@Viaasta]

Hey Dr. Tisdell, I was wondering if you did end up making a video on the derivation of the Fourier transform and subsequently the Inverse Fourier Transform. PS. This video helped a lot, thank you so much!

[@gaspernovak3540]

Nice video! Thanks for good examples of using fourier transforms.

[@GoutamDAS-ls1wb]

I learn so much from these videos--can not thank you enough Professor Tisdell! I wish my math teachers had as much energy and enthusiasm as you do. I have a question regarding Integ^(-z^2) dz, where z is a complex variable--is the math just like integration over a real variable?

[@abhayc7027]

Square on a was lost when it was separated and multiplied with a

[@gosipathulachinnapamuleti1309]

thank you sir.this helps lot and i hope that you may upload total lecture regarding mathematical physics.

[@letslive6176]

Thanks sir,it really helped a lot.

[@johnquest3102]

Hello professor, THANK YOU, i really appreciate this series, i studied (as tech elective) Laplace transforms and Fourier series in college and I am studying Fourier transforms now (32 years after graduating) so my question is: what does an i in the result mean? Sometimes all the i cancel out and sometimes not, sometimes there is an i in the exponent. The problem I want to solve is the FT of the N-wave of a sonic boom (sudden rise in pressure followed by linear decline to negative pressure and then a sudden rise to ambient pressure) but it troubles me that there can remain an i in the result, it would seem that every i should resolve in to a sin or cos term. Best regards, John in Michigan.

[@owlsmath]

That was great! Thanks for the explanation.

[@dennistu]

I got a question, on the wikipedia page for the Fourier Transform, the formula is simply the integral from -inf to +inf, but in this video it is multiplied to 1/sqrt(2*pi). Does anyone know why is that?

[@DrChrisTisdell]

04:37

[@dennistu]

Dr Chris Tisdell Thanks, I missed that.

[@PauloConstantino167]

I love Chris Tisdell :)

[@omaralnajjar4920]

You are amazing. This is super clear. Thanks.

[@1990MrAnderson]

Chris, great video, however, when you completed the square, why was ((iw)/(2a))^2 - ((iw)/(2a))^2 = w^2 /4a and not zero??.. Am I being stupid or can you or anyone explain.

[@fun2badult]

The second term (iw/2a)^2 turns into (i^2)(w^2)/(4a^2). Due to i^2, it turns the second term into a positive term. So it becomes (iw/2a)^2 + (w^2)/(4a^2). Then, since there's an 'a' outside, when we bring the second term out, the bottom one of the a^2 gets cancelled and you end up with (w^2/4a)

[@LittleLotte5]

Hello!! Can you explain why (a -jw) (a + jw) = a2 + w2 ? Where is the j? Thanks a lot!

[@gerontius1726]

j (or i) is used to denote the imaginary square root of minus one. When the two brackets multiply together they give you a squared + (-j)(j) w2 (which equals a2 + 1*w2. This is simply complex number theory.

[@Captain_Rhodes]

so if we are given a signal to transform which coefficients do we use?. surely using either 1 , 1/2pi or 1/sqrt(2pi) will all give different results!!! i realy dont understand that. say i am given e^2t and told to transform it - which one do i use??

[@neelmodi5791]

the transform itself will be different, but its effect in the PDE will still be the same

[@Captain_Rhodes]

oh god dont start that,. what does PDE mean. pretend im a child please

[@neelmodi5791]

It stands for partial differential equation If you've heard of the Laplace transform, it's goal is to reduce the derivative terms. A Fourier transform's job is similar and doesn't get affected by the coefficients of the integrals

[@Captain_Rhodes]

ok so basically if i get 2 answers - one says 1/2pi times something and the other sats 1/sqrt(2pi) times the same thing they are both the same, even though they have different amplitudes?

[@neelmodi5791]

They aren't the same, but they will give you the same result when you use them

[@MoiLazarus]

Where is the practical application of the transforms. I thought, as the introduction, it would highlight the concept from the very basic understandings before delving into highly complex integrals. Thanks.

[@DrChrisTisdell]

@@MoiLazarus if you listen to the first 60 seconds then I say the motivation is to solve partial differential equations. 👍👍👍

[@martinchukwuezi8590]

Very good. I enjoyed the class

[@elvis33060]

More examples pls

[@KatherineRenshaw]

you are a saviour

[@Internet-Antics]

Very helpful! Thank you again!

[@waqardetho2426]

how dz = root(a) dx

[@ura239]

Fascinating! ....thanks again.

[@bahiraborhan7068]

many thanks , this video is really helpful for me

[@bhavnanm1017]

Thanks a bunch for this! very well explained.

[@hithyshias3474]

Wow it went into my mind sooo easily😍

[@kevinwilfriedngouan6344]

there's a confusion between Fourier transform and the Fourier inverse !

[@mace_in_your_face6230]

Thanks very much, 4 more assignment questions to go ^_^

[@ArvindSastry]

Thank you! It was extremely helpful!

[@DrChrisTisdell]

Many thanks. It is my pleasure.

[@pemulung]

My god .. Thanks Dr. Chris ... I asked about FT maybe year ago ....

[@lucyatieno706]

Very exciting,eng. math.I am pressing your cloths!

[@rayssalinhares7476]

thank you a lot.!!! you helped me a lot!! im from brazil.. thank you so much for this video.. you are awsome!

[@rohithl9291]

God! thank you soo much! saved my day!

[@aurangzaibkhan8680]

THANK YOU SIR....... RESPECT...

[@shshsbksyshshshn5146]

Thank you for this!

[@elianlidodeasis7246]

13:20

[@dartmouthskater25]

I think youre missing a letter on your last name

[@jay714ful]

i appreciate that you invested your own time to teach this but i must say if your going to attempt to teach it you must do so properly. For instance you said the integral converges without even mentioning what converges meant

[@DrChrisTisdell]

+jay714ful Thanks. I can't mention everything, so I need to make decisions on what to leave in and what to leave out. I do assume that viewers understand what it means for an integral to converge. (Convergence of integrals is usually taught in a Calc 1 course, which is a long way from Fourier Transforms.)

[@jay714ful]

Hmm I respect and understand your point on the matter. However when using youtube as a forum to teach, one should expect that most of the viewers will not be well versed in the subject and will not have the conventional academic understanding and ordering of its contents. Therefore I feel it is paramount that one does not simply leave holes in his explanation as he is working under the ( false ) assumption that his audience knows how to fill them. In such instances a relatively short exposition would serve to further intellectually enrich those who use the resource. Thank you.

[@mace_in_your_face6230]

+jay714ful Why are you studying fourie transform if you dont even know what integral converges means?

[@jay714ful]

well i suppose in a very ironic way its because I know something you don't.

[@mace_in_your_face6230]

ok

[@thn262]

Thanks a lot!

[@hamadmushtaq4123]

Awesome thank you very much

[@calvinjackson8110]

They are "elementary" to YOU! To those like me who do not have a clue to what it means, how it's used and what it is all for its mind boggling.

[@albertoscalici8235]

Thank you so much

[@basantkumargupta9194]

Very nice

[@Stat1onary]

This one saved my ass

[@TM-Yan]

thank you :)

[@Ragingwasabi9000]

that was only the introduction? im out

[@abdelrahmangamalmahdy]

lol

[@playablou8430]

je ne comprend pas l'anglais , mais j'ai tout comprit . Mieux vaut l'accepter cette transformation de fourrier. Moi je l'ai comprit en tant que ''recherche de la composantes sur une base de fonction etc .. f . e = x ( composante) ..en faite c'est plutôt : x = 1/2pi ( F) avec F transformée de fourrier .;

[@mdnasiruddin700]

wow, you made it water.

[@alistairdouglas9430]

good video, but b careful your house is haunted i can sense it

[@insearchof9090]

great

[@talhatalha3308]

NICE

[@The112Windows]

Yes!!

[@bruceboice9007]

Good Shit!!!

[@wadeli4726]

I do not want to go to university any more,

[@hithyshias3474]

Wow it went into my mind sooo easily😍