The Fourier Transform- Part III

A short tutorial video on how the Fourier Transform works. The video is designed for those who know what a Fourier Transform is but need to understand at a basic level how it converts time domain signals into the frequency domain.

Category:

Education

Tags:

• electrical
• engineering
• fourier
• transform
• time
• domain
• frequency
• signal
• analysis

[kridnix]

Yes, the magnitude-phase is actually the more common way to represent the signal since it can be hard to tie real-imaginary representations to actual physically measurable variables, at least in my field.

[protikmaitra]

The very last slide (9:10) looked like a Gabor Filter.

Q1. I was wondering how I could make a Fourier Transform or Gabor Filter Response more robust by exploring different phases. Is it necessary? Could you please recommend some short cuts that are fast? The only option right now for me is to code it out.

Q2. What if the input signal is sinusoidal but entirely positive?

Q3. What is the frequency if the spikes in the real and imaginary parts (8:16) do not coincide? Is it possible?

-Thanks-

[kridnix]

@protikmaitra For Q#1 I have no idea since I am not a signals guy. I would try to code this up using some sort of genetic algorithm but that is just me not knowing this area. Q#2: This is a sine wave plus a DC component. Since the FT is linear it is a delta function in frequency plus a large spike at frequency zero that is meaningless. Q#3: I believe they need to coincide or else the signal isn't causal. You can manipulate numbers to create signals that couldn't exist in physical systems

[extremedavo1979]

This was a purely mathematical explaination of the algorithm. He does not explain all the implicaitons of Fourier analysis in a practical signal analysis sense i.e. nyquist, sampling etc.

[kridnix]

@extremedavo1979 That is absolutely correct. In less then 30 minutes I would have a hard time explaining the practical implications of the Fourier Transform in a way that was more than a brief overview.

[kridnix]

If you want to write software check out "Numerical Recipes in X" where X is either C, C++, or Fortran

[dilish1]

really awesome......simple and informative....

[ryeryeeect]

My head hurts after watching these three videos. Is this what it means to learn something. After all my time in college I am confused, I have never felt this sensation before. :D

Thank you for the video's they are greatly appreciated, its nice to see educators who go above and beyond only for the sake of educating.

[erjavedshaikh]

awooooooooooosome all three videos were really helpful. Thank you sooo much

[adastra123]

What a talented teacher. I get it !!!!!!!!!! after years of not getting the whole picture , I finally get it !!!!!!!!!!!!!. Thanks a million , I feel confident about all that stuff now . You are worth a thousand shrinks when it comes embuing to self confidence. I am going to have a banana now to celebrate. Thanks for those videos , you are a gifted teacher , thanks so much.

[SnatThatBat]

I logged in just so I could like this. "Think of it as an algorithm." changed my life

[seniorbooboojuice1]

Thank you so much sir! I learned what the Fourier Transform really is from you! I'm grateful

[GarbageDevon]

Thank you so much for posting this! I really learned a lot.

[Zanneth]

These videos really helped a lot, thanks!

[igormon]

Do you have any videos on signal sampling and quantization? I couldn't find any in your channel.

By the way your video was very helpful.

[rudymanuel]

thanks so much ...its a very good video , i see that you use matlap to help understand the waves in real and unreal , i speak spanish , but the way you do that is exelent , I'm studing electric engineering , and it help me a lot !!!

[Arlesterc]

Good video on a difficult topic. However I got lost at about 2:28. I am not sure what the multiplication is that makes the sine term disappear in the top diagram. It seems that the multiplication would be {3sin (3Hz) +.8cos(8Hz)}*cos(wt)(3Hz) which works out when distributed to be {3sin (3Hz)*cos(wt)(3Hz)} +.8cos(8Hz)*cos(wt)(3Hz). It seems that first term here goes go 0 - I don't get it. Perhaps an example with actual numbers might help me. Any time taken to respond is appreciated in advance.

[yngwievanhendrix]

This was the best explanation of FT ever.