Fourier transformation is a technique that decomposes a given sequence into multiple elements that correspond to a specific frequency. The given input is a time series signal such as audio data. Fourier transformation calculates the magnitude of each component corresponding to the frequency. The basic assumption behind Fourier transformation is that every periodic function can be represented as the weighted summation of simple curves, such as sine or cosine functions. While we can decompose any function by multiple polynomial terms with Taylor expansion, Fourier transformation allows us to disintegrate the periodic function with multiple cosines or sine components. Although this is a pretty plain assumption, it is powerful enough to allow us to perform mathematical analysis for any kind of signal value that shows a periodic pattern.
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