Fast Fourier Transforms: Theory & Practice

In our Fourier Series class, we designed out own project to play with Fast Fourier Transforms (FFT) to capture descriptive frequencies of an input signal in order to recognize that signal later. Due to patent sensitivity, I will not go in depth of the algorithm.

  • I implemented the “spectrogram” recorder:
Aphex Twin's face from "mathematical equation" song

Aphex Twin’s face from “mathematical equation” song

  • Observed some fun results:
Guitar Shift spectrogram

Guitar Shift spectrogram

  • Represented sound in low dimensional form:

    Low Dimensional "face"

    Low Dimensional “face”

  • In order to eventually map input sound to original song’s database (Shazam algorithm):

    Matched input and recorded fragments

    Matched an input sound fragment to the song in the database

More Intuition About FFT on Presentation Slides.