1. Frequency representations
1.1 Representing functions
First of all, we need to clarify the meaning of the word "tool". Today's mathematicians have a multitude of techniques for analyzing, synthesizing and representing any number of functions using elementary "building blocks". These techniques for harmonic analysis in the broadest sense are sometimes combined with high-performance algorithms, making them even more useful for numerical applications.
The most fundamental example is certainly the Fourier transform, known since the 19th century: this consists first of all in performing a frequency analysis of a function f (t ), by...
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Frequency representations
The time-frequency approach
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