Abstract
Back in the early 1800s, the French mathematician Joseph Fourier discovered that any periodic fucntion can be expressed as a (possibly infinite) sum of sines and cosines. This surprising fact is now known as Fourier expansion and it has many applications in engineering, mainly in the analysis of signals. It can isolate the various frequencies that underlie a signal and thereby enable the user to study the signal and also edit it by deleting or adding certain frequencies. The downside of Fourier expansion is that it does not tell us when (at which point or points in time) each frequency is active in a given signal. We therefore say that Fourier expansion offers frequency resolution but no time resolution.
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© 2010 Springer-Verlag London
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Salomon, D., Motta, G. (2010). Wavelet Methods. In: Handbook of Data Compression. Springer, London. https://doi.org/10.1007/978-1-84882-903-9_8
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DOI: https://doi.org/10.1007/978-1-84882-903-9_8
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