# ELI5 : Fourier Series

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Tech2025

Gold Member
What's the question?

Tech2025
What's the question?
What are Fourier Series in layman's terms ?

Gold Member
What have you found out and read so far?

Tech2025
What have you found out and read so far?
Basically what I understand is that it is a method to find different parts of a continuous signal.

Gold Member
Hmm. The Fourier Transform transforms a signal in the time domain (a varying voltage or whatever) into the frequency domain (a set of frequencies). It strictly applies to an infinitely long signal (with no beginning or end) and the resulting frequency domain signal can consist of a continuum of values.
Engineers use a Discrete Fourier Transform and that assumes a repeating g signal which you represent by a fixed number of values in a time window - say a sampled waveform from an electronic organ note. The DFT gives you a set of values of frequencies in that signal and the frequencies are all harmonics of the fundamental note. At its simplest, it would correspond to the draw-bar settings on an old fashioned Hammond Organ which give a particular audio wave form.
The Fast Fourier Transform is just a smart way to speed up the Fourier analysis by always using a number of samples that is a power of 2. i.e. 256 samples or 2048 or as many as you lime, depending on the accuracy you want. Single chips are available that will do that for you.

Tech2025
Tech2025
Hmm. The Fourier Transform transforms a signal in the time domain (a varying voltage or whatever) into the frequency domain (a set of frequencies). It strictly applies to an infinitely long signal (with no beginning or end) and the resulting frequency domain signal can consist of a continuum of values.
Engineers use a Discrete Fourier Transform and that assumes a repeating g signal which you represent by a fixed number of values in a time window - say a sampled waveform from an electronic organ note. The DFT gives you a set of values of frequencies in that signal and the frequencies are all harmonics of the fundamental note. At its simplest, it would correspond to the draw-bar settings on an old fashioned Hammond Organ which give a particular audio wave form.
The Fast Fourier Transform is just a smart way to speed up the Fourier analysis by always using a number of samples that is a power of 2. i.e. 256 samples or 2048 or as many as you lime, depending on the accuracy you want. Single chips are available that will do that for you.
Thank you! Finally something that made sense