# Fourier analysis explained

2005-01-23

Miranda has a good and enlighting explanation on the inner workings of Fourier analysis. Even if I’ve read math theory of Fourier transforms earlier and know what kind of information Fast Fourier Transforms yield this provided new insight:

*Fourier analysis detects the harmonic components of a sound using a pattern-matching method. In short it functions by comparing a self-generated *virtual signal* with an input signal in order to determine which of the components of the former is also present in the latter. Imagien a mechanism whereby the components of the input signal are scanned by multiplying it by a reference signal. For instance if both signals are two identical sinewaves of 110 Hz each then the result of the multiplication will be a sinusoid of 220 Hz but entirely offset to the positive domain. The offset value depends upon the amplitudes of both signals. Thus it is also possible to estimate the amplitude of the input signal by taking the amplitude of the virtual signal as a reference.
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*The mathematics of the Fourier transform suggest that the harmonics of a composite signal can be identified by the occurrences of matching frequencies whilst varying the frequency of the reference sinewave continuously. The digital version of this method might be simulated on a computer by scanning the input signal at rates that are multiples of its own fundamental frequency. This is basicly how FFT works.*

p. 52-53

I made a Max patch to investigate this today. You can download "by clicking the image here.

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