Math: Understanding the Fourier Transform

Play a pure tone on a computer and you hear a clean clear note. A perfect single sound. Take a number of pure sounds and you can create something quite complex.

Did you know that given a complicated sound you can decompose it back into the different tones (or frequencies) that make up the complicated sound?

The technique is called the Fourier Transform. It's not as complicated as it sounds. At least the overall theory is not too complicated to understand.

The DSP dimension has an article entitled The DFT "A Pied": Mastering The Fourier Transform in One Day. The on again, off again, on again blog called Physics For My Mom has a multi-part overview of the fourier transform.

• Fourier analysis 1 - Sound waves
• Fourier analysis 2 - More complicated sound waves
• Fourier analysis - Sines and integrals
• Fourier analysis - Sines and integrals (part 2)
• Fourier analysis - Sines and integrals (part 3)

That should be more than enough to get you started on fourier transforms. Once you understand that theory jump ahead and see if you can explain the math behind FFTs to me.