I thought that fourier transform of a function is by integrating dividing the function by basis functions in the form e^(jwt) in the denominator and hence the negative sign when goes to the numerator. Thank you for this explanation. This kind of analysis is not found anywhere else but this channel.
@@iain_explains yes, lin 1/2 were my fav class. prof made it very challenging but I thank him for it, bc I learned a lot. just graduated in May, and he recommended me a systems engineer position. got hired!
Thanks, when we are in the complex plane, we can denote a complex number as A*exp(j*phi). I learned that phi was the argument (angle). When we bring in the time that phi contains also frequency and time, so that we get A*exp(j*w*t+phi). We have substitute phi by a more complex expression - is that correct?
Yes, that's right. Here are two videos that will provide extra insights/explanation: "Why are Complex Numbers written with Exponentials?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Cy5IQnBpJoA.html and "How do Complex Numbers relate to Real Signals?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-TLWE388JWGs.html
Hi Iain, great video again. This feels like its really clearing up alot of holes in my understanding. I think a more general question I had thats not "why is the negative sign in the fourier transform" is, "why does there need to be a negative sign in either the FT or the IFT?" It seems like during the video the ending conclusion was "it could be either, but it needs to be one." I mean, both the IFT and the FT would produce an orthonormal basis set of vectors, regardless of the negative sign, so why does a negative sign need to be in one of the two in the first place? Thank you!
Ideally you want a transform to be two-way, or 'reversible'. So that you can transform into the new domain, do some maths in that new domain (that might be "easier" to do in that domain), and then transform back to the original domain. That's why you need a +ve in one "direction", and a -ve in the other "direction".
No problems. You're making lots of great comments and suggestions for improving the website. I really appreciate it. I'm glad you're finding the videos helpful.
@@iain_explains I know you've heard plenty of these. You have done an amazing job in content and explanation. I am gonna go through another 30-40 videos and then maybe I send an email with some suggestion. Your website and content definitely deserves more audience. I do love the fact that you handle this channel like a classroom and answer all questions (no matter how stupid they are). Not sure how it scales when you have 100K+ follower.... but problem for a different time ;) have a wonderful weekend, ... well I guess yours started already.
omega = 2pi f , so d(omega) = 2pi df , so if you consider the FT equation written in terms of f, and then do a change of variables from f to omega in the integral, you will get a 2pi factor appearing.
