Principles of Analog Electronics

Mathematical Tools

21

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 dened 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 ...