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 of the FFT  

Book: How the Fourier Series Works
https://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