
Mathematical Tools
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When the function to decompose is not periodic, the Fourier sum turns into an
integral. Therefore, we will no longer discuss a series, but instead Fourier’s inte-
gral, which can be considered a generalization of the series. The decomposition of
a function with Fourier’s integral is dened as the Fourier transform.
Observation
The signals that we handle are typically variable with continuity in time.
Therefore, it appears appropriate to represent and mathematically analyze sig-
nals in the time domain. However, in practice, it is preferred to operate in the
frequency domain, and it is possible to decompose the signal to its funda ...