Complex numbers and Fourier series

[MSAKARIM]

What are the benefits of complex numbers, Fourier series and Fourier transform in practical life?

 

[hobbyckts]

Complex Numbers - https://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html
Fourier Transform - https://www.askamathematician.com/2012/09/q-what-is-a-fourier-transform-what-is-it-used-for/


fourier series -
1. Signal Processing. It may be the best application of Fourier analysis.

2. Approximation Theory. We use Fourier series to write a function as a trigonometric polynomial.

3. Control Theory. The Fourier series of functions in the differential equation often gives some prediction about the behavior of the solution of differential equation. They are useful to find out the dynamics of the solution.

4. Partial Differential equation. We use it to solve higher order partial differential equations by the method of separation of variables

 

[_Eduardo_]

They aren't tools for practical life.

For electronics, they are useful tools for analyzing and understanding the signals behavior.

For freshmans, an infinite source of pointless questions.

 

[D.A.(Tony)Stewart]

These are used daily to understand everything better.

- complex numbers are used for everything from RF to AC energy distribution to separate reactive power (LC) from real power (R). it also is representing phase shift with frequency that always exists in filters and and bandwidth limited circuits.

Fourier series helps to understand to understand signal, power and mechanical systems in both time and frequency domains. This is then used to design filters, shock absorbers, problems with bearing frequency wear.

here play with this using mouse in time or frequency domain.
click log view and select signal or draw any arbitrary signal or spectrum and phase
https://www.falstad.com/fourier/

 

[andre_luis]

What are the benefits of complex numbers, Fourier series and Fourier transform

Complex numbers and Fourier transform, as well many other math artifacts are tools that allow us to perform algebraic operations in an easiest fashion. In certain sense, we can understand it as converting the original complicated domain in a simplest arrangement aimed to achieve the result by simple calculations, but once finished, returns to the original domain.