I am a high school student doing a project in Fourier transform. I was planning to learn Fourier transform and manually apply the calculations to a section of a song and see what I get. However, I need to learn Fourier transform on my own and most tutorials I found are on expanding square wave etc, which isn't very helpful for my plan (now seems too ambitious) as I will be dealing with aperiodic waves.

Moreover, I was seeing all those different types of Fourier transform (DFT, CFT, STFT....) I am a little lost as to how to apply the formulas and what type of Fourier transform should I learn to analyse the sound wave of a song... Can anyone give me some suggestions?

  • $\begingroup$ You probably want a spectrogram rather than just a fourier transform. It's a little more complicated, but it produces something to look at that you could make sense of. Many software packages can do this. So, basically, as a start, find software that you think you can use that can produce a spectrogram. For example, Audacity can do this, or something like Python and Matplotlib. $\endgroup$
    – tom10
    Apr 29 at 16:07
  • $\begingroup$ Don't start with something complicated like real audio data. Can you Fourier transform a single sine wave? What about a Gaussian? Slowly build up on some examples that can be done analytcally before you try to handle something noisy. $\endgroup$
    – Andrew
    Apr 29 at 16:25

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