– what is the fast Fourier transform in relation to audio processing?

In: 7

The Fourier transform converts Signal vs Time to Intensity vs Frequency, effectively breaking the signal into it’s frequency components. The fast part of FFT is a particular algorithm that makes it easier for computers to do this conversion. The intensity vs Frequency graph is useful for finding particular noises like clicks etc. You’ll recognise the spectrum analyser is the result of an FFT.

I’d say with respect to audio in particular, the Fourier Transform will tell you how loud (amplitude) the sounds of different pitches (frequencies) are in each short section of music.

If you make the section of music you transform at a time longer you can separate the pitches more finely, but as a result it will be an average over that longer period of time.

The Fast Fourier Transform (FFT) is just a computationally efficient way of performing a Fourier Transform with a digital computer.

I find this picture helpful:

https://www.nti-audio.com/portals/0/pic/news/FFT-Time-Frequency-View-540.png

As you can see, it takes all the frequencies that are appearing and shows it as amplitude.

FFTs are popular for measuring audio gear as distortion is just unwanted frequencies besides the frequencies you want, so if you play a 1kHz tone, any other tones showing up will be distortion.

[Here is an FFT of a speaker amplifier with low distortion](https://www.audiosciencereview.com/forum/index.php?attachments/topping-la90-measurements-low-gain-integrated-amplifier-high-performance-png.202314/)

[Here is an FFT of a speaker amplifier with high distortion](https://www.audiosciencereview.com/forum/index.php?attachments/smsl-sa100-bluetooth-amplifier-audio-measurements-png.37977/)

The fast Fourier transform is a tool that helps people who work with sound to understand what kind of sounds are in a piece of music or other audio recording. It does this by breaking down the sound into tiny parts and figuring out what kinds of sound frequencies are present in each part.

This is helpful because different frequencies of sound can make a big difference in how a piece of music sounds. For example, high frequencies can make a sound seem bright or sharp, while low frequencies can make it seem deep or booming.

The FFT is like a special microscope that lets us look at a sound and see all of its different parts, so we can understand it better and do cool things with it, like making it sound different or removing unwanted noise.