thank god, an indepth proof, all the other videos I was watching were glossing over what was going on with creating the integral from the rieman sum, usually you get a definite integral and I didnt understand why we were getting an indefinite integral untill seeing the L to infinity and bounds of BOTH integrals like you have here, thank you much
Thank you, as someone studying mathematics I was curious how one would go about deriving the Fourier transform and you have done an excellent job explaining this.
Im confused, why does omega run from minus infinity to plus infinity. It is defined to be pie times n over l, and both n and l aproach some infinity. I am pretty sure that omega is supossed to be an undefined number.
A few typographical errors here and there, but you also provided the clearest explanation of the Fourier transform I’ve probably ever come across. I really appreciate your decision to post this for the internet population to learn from. I should mention that your brief statement of the inverse Fourier transform hurt...it would have been wonderful for you to extend your analysis to that inverse transform. All things considered, I’m very happy with your work (not that you need my approval lol). I hope you keep up the awesome education. Best wishes from a new subscriber,-Float Circuit.
Hi, Really great video explaining the Fourier Transform. I'm just wondering how the F(omega) function went from having 1/2L to having 1/2pi when the integrating bounds changed from -L to L, to -infinity to infinity? Thanks
In the first summation, it does not make any sense the "e^(i*theta*x)" becomes "e^( - i*theta*x)" when he replace "n" by " - n". Would you explain it ? It is really unclear
Because its the hermitian series, which have the symetrical property for complex conjugate, it falls under complex analysis category, TL;DR its the same as original series
If you look to the definition of An and Bn and substitute n by -n, you see that A(-n) = A(n) (cos is an even function), and B(-n) = -B(n) ( sin is an odd function), hence you get A(-n) -iB(-n) = A(n) +iB(n). Then C(n) is just (A(n) + iB(n))/2
I viewed many videos on Fourier transform and I found in some videos that there werer 1/√2π ,1/2π and in some videos there was nothing Its very confusing for me
Shahmeelbhai Shahmeelbhai although a year old and you may have figured it out 1/sq(2pi) is just an arbitrary normalization constant which makes the integral =1
