Fourier Transform and Inverse Fourier Transform: What's the difference?

Explains the difference between the Fourier Transform (FT) and the Inverse Fourier Transform (IFT), and explains why there is a negative in the exponential function in the FT.

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[mnada]

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.

[gunhwimoon]

Thank you always. I feel like you already know what I would study about.

[Julia-huxe]

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?

[momoghanem]

Why integral sin(omega*t) always equal zero? What if w=pi/(2*t_bar), then when t reaches t_bar (t=t_bar), sin(w*t)=sin(pi/(2*t_bar)*t_bar)=sin(pi/2)=1, and the integral then becomes equal to infinity. Isn't that correct?

[brian]

good explanation, brings me back to my days in linear systems 1

[jamesb]

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!

[bobbaberson]

Hi Iain, both the summary and the video itself is missing in the website under the fourier-related lectures.

[KSMK]

I still don't understand why we use the scaling 1/2π