Preview: Negative frequency, imaginary numbers and the complex conjugate

Ask any mathematician why the Fourier Transform of a signal produces a magnitude spectrum containing negative frequencies, and they will probably answer: because your signal is real. "Well of course it’s real! You might be thinking. I didn’t imagine it!" The thing is, what you mean by “real” and what a mathematician means by “real”, may not be the same thing.
In this preview, we look at what mathematicians actually mean when they talk about real signals and why negative frequencies make them real.
In the full version of the video, we'll go into more detail about what negative frequency actually is. We'll look at the role the Inverse Fourier Transform plays in the process, and I’ll also be showing you a physical effect of negative frequency in the real world, in case you thought that it was just a quirk of the maths.
The full version of the video is currently in production and will be available in a few weeks' time.
Playlist: Understand the output of the FFT
• Understand the output ...
Book: How the Fourier Series Works
www.amazon.com/dp/B0B1BY5H6T
0:00 - Introduction
0:12 - What makes a signal real?
1:05 - The Fourier Transform
2:29 - Where does negative frequency come from?
3:15 - The Inverse Fourier Transform
3:50 - The complex conjugate
4:49 - What to expect in the full video
5:10 - End Screen

[@MarkNewmanEducation]

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[@dilex123explorations]

Very educative one here ,Mark,Thank you.

[@MarkNewmanEducation]

Thanks. It was great talking to you in our interview: th-cam.com/video/Q6jDGikk4hw/w-d-xo.html

[@francoisgarcia7457]

Thanks for these interesting videos!

[@dddderek]

What a teaser! I can't wait for the full video!!! Thank you so much for making this content. 👍👍👍

[@MarkNewmanEducation]

You're welcome. Working on the full version as we speak. It should be out before the end of July.

[@dddderek]

@@MarkNewmanEducation I graduated in EE 26 years ago, #1 in my class, but didn't truly, intuitively understand anything. Now, so much later in life, I'm becoming passionate about understanding things from the ground up, in my gut, through and through. Your videos are tremendously helpful, and I wish I had a teacher like you back in my college days.

[@longluo1788]

Thank you, mark!

[@MarkNewmanEducation]

You're most welcome. Please share.

[@nareshkumar4207]

Hi. Please also explain concepts with some problems from text books. It will good to learn.
Your videos are so good. And I follows you continuously. You are great.

[@MarkNewmanEducation]

Will do. I'll make a note for future videos. Thanks.

[@muddassirghoorun4322]

At 04:10, why is the - 0.32 pointing to that time specifically. Most certainly, then there will be more 5 & -5 Hz frequencies corresponding to other times in the IFT list. Is that correct or have I missed something?

[@MarkNewmanEducation]

In the example, I simply calculated the instaneous value for a random point in time using the inverse Fourier Transform. The 5 and minus 5 Hz frequencies can be calculated for any point in time and they will give a different value depending on the value of t. I just chose one particular value of t for the example.

[@muddassirghoorun4322]

@@MarkNewmanEducation Thanks for the answer.

[@martinsanchez-hw4fi]

At 1:16, shouldn't a pure sine wave only be formed by sine components?

[@leonardomaia7661]

a sin wave is equal a cos with a phase of -pi/2