1. Adam Mraz Joe Castagneri Denis Kazakov
FFT to recognize music
Adam Mraz
Joe Castagneri
Denis Kazakov

2. Plan
Theory
Practice
Motivation

3. Theory

5. Complex Exponentials

7. DFT

8. Divide & Conquer

9. O(N*log(N)) - complexity

10. Practice

11. Guitar string
(audio + visual)

12. Guitar Shift
(audio + visual)

13. Detail Level
When you listen to music, your brain is good at recognizing the sound as a whole.
High sensitivity: Even if one instrument is a little off, director would be quick to spot it.
Low sensitivity: I don't play music instruments and if I suddenly started playing piano, I would probably never notice that it could be out of tune, because I just don't capture sound with that precision.
High
Low

14. Low Dimensional Representation of Sound
That level of precision of your brain could be mimicked from algorithmic perspective.
Image 1: similarly, guitar string
Image 2: IP of image 1

15. Demo

16. Original:
Recorded:

17. Original:
Recorded:

18. Example Song Analysis
(audio + visual)

19. Motivation Periodicity can be captured
Patterns of periodicity can be recognized
Fingerprint recognition - even though now, neural networks are beginning to get more accurate than almost any method, it is possible to capture for example fingerprints using FFT on images.

20. 1D

21. Signal Processing

22. 2D

24. The points and lines away from the center are a signature of the periodicity in the image. We remove all those and retain only the centre, which contains the information about the low spatial frequency (that is, high size) components of the image:

26. We can now do an inverse Fourier transform of this:

27. Image Compression

28. 3D

29. Waves Simulation