Introduction to the Fourier Transform (Part 2)

This video is the second part of the introduction to the Fourier Transform. I address an error that I made in the first video concerning the scaling term of the transform. I also try to give you a way to think about the forward Fourier Transform as just a division of the time domain signal and sines and cosines. If you have any questions on it leave them in the comment section below and I'll try my best to answer them.

I will be loading a new video each week and welcome suggestions for new topics. Please leave a comment or question below and I will do my best to address it. Thanks for watching!

Don't forget to subscribe! Follow me on Twitter @BrianBDouglas!

[AljazJelen]

Hi Brian!
So as a Mechanical Engineer, we never really dug deep into Fourier. Short overview and then straight to Simulink and FFT libraries... all in discrete domain.
However, now I work in Automotive industry on electric vehicles, dealing with topics that i never really studies. Long story short, we often need to define parameters of SW and HW elements, which contribute to different delays and phase shifts (simple LPF). Diving from analog to digital has always been intuitive to me, but I wanted to 100% understand the background of Control Systems, Digital Signal Processing...
Recent situation of quarantine "finally" forced me to do a step... and man... I am happy I did. With my "rusted" knowledge I started from scratch and finally got to the point, where I understand the main principle. All this is in 2 afternoons!
Thank you for putting an effort. Explanations really feel like they were designed to focus on listener's basis and gradually build up the comprehension of the topic.

Best regards,
Aljaz

[bradlane]

The analogy of dividing $15 by the $5 bills is great! And then applying it to the F.T. has just made this, make much more sense. I just had a 2 month class on Signals, in which we used a lot of FTs, which i now understan a little more. Thank you!

[kashishsheth]

Thanks for spoiling my plan to Complete revision in less than 3 days. Each 10-15 mins lecture takes me around 30-50 mins! However, I have never been so happy for having my plan spoiled!
Cheers Brian for such an amazing work!

[nmbileg]

man this lecture is ten time useful than college class... thank you mr douglas, so appreciated

[pumpkinhead]

senior computer engineering student here:   I have been struggling with the intuition behind fourier series and transforms for a while now, but the part at 6:00 and specifically at 6:14 just pieced it all together. 

Thank you!

[alakbakbak]

They way you compared finding the frequencies in a signal like dividing $15 into $5 bills made everything so clear. Thank you!

[looksintolasers]

You've got a gift for explaining these things intuitively. Thank you.

[HassanAli-ospy]

Best explanation of the Fourier series/transform I've ever come across! Marvelous!

[daviddieken]

wow i have memorized the formulas without a clear explanation from professors as to why it works or how it came to be. thank you from the bottom of my heart for taking the time to putting together such amazing videos to help people all over the world learn and grow.

[BrianBDouglas]

Forward FT goes from time domain to frequency domain, inverse does the opposite.

Fourier series breaks a periodic time signal into the frequency domain. It does the same thing as the FT but the transform works with non-periodic signals.

Yes X(v) and F(v) are the same. I'm really bad about using the same variable letter from video to video.

Scaling is not amplitude. If you plot the complex output of the FT amplitude is the distance from the origin. Scaling is just a gain part of the equation.

[Fransamsterdam]

This is the best way to use a blackboard on youtube I have ever seen. Congratulations!

[BrianBDouglas]

Great catch San! Starting around 1:15 I accidentally wrote dt instead of dv. I'll put an annotation in there so others aren't confused. Thanks!

[ConnorHofius]

Watching this in 2021 and this still makes so much more sense than what my professor says in class...

[Runzolf]

The sequence where you plot the power of the multiplied sines is what did it for me! I'm already graduated but damn how many things I took for granted! Thanks a lot!

[ozomata]

Mind=blown
the first part was like magic, yet made lots of sense
Thanks

[am-i-ai]

I understand the Fourier Transform so much better now. Thank you! :)

[absurdsun]

I reaalllyyy got goosebumps when you explained the division analogy!!

[hugeride]

Amazing. I understood more in 13 mins of this video then I did by reading 2 books.

[tejesdas]

Thanks Brian.Both part 1 and part 2 are well presented, albeit bit fast for my pace of understanding.

[juniorcyans]

I’ve been lucky to find your channel. Thank you so much for demystifying it! What I want is not just knowing how to use it, like a monkey imitating humans, but understanding why. Thanks again!