The Fourier transform is not limited to functions of time, but the domain of the original function is commonly referred to as the time domain. If a frequency is not present, the transform has a value of 0 for that frequency. For each frequency, the magnitude ( absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that frequency, and the argument of the complex value represents that complex sinusoid's phase offset. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. A pitch detection algorithm could use the relative intensity of these peaks to infer which notes the pianist pressed.Ī Fourier transform ( FT) is a mathematical transform that decomposes functions depending on space or time into functions depending on spatial frequency or temporal frequency. The remaining smaller peaks are higher-frequency overtones of the fundamental pitches. The first three peaks on the left correspond to the frequencies of the fundamental frequency of the chord (C, E, G). This image is the result of applying a Constant-Q transform (a Fourier-related transform) to the waveform of a C major piano chord. An example application of the Fourier transform is determining the constituent pitches in a musical waveform.
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