Linear circuit investigation using FFT

The Fourier analysis is very powerful and useful instrument of investigation that is used widely in many scientific applications. It named after French mathematician Joseph Fourier who proved that arbitrary signal can be represented by sum of harmonic signals. Each harmonic signal (sinus or cosines) has own frequency, phase and amplitude. Нarmonic signal keeps its shape while passing through the linear circuit and change only amplitude and phase. This ability makes the Fourier analysis to become a power method of investigation. To perform Fourier analysis on computers in digital form the Discrete Fourier Transform (DFT) was developed. The fast optimized version of DFT is called Fast Fourier Transform (FFT).

Solving ordinary differential equations

How to solve systems of linear differential equations? Here we describe three ways: Runge - Kutta method, and two similar ways to each other using the method of state space.

Let our process is described by the following differential equation:

Fast Fourier Transform (FFT) simple usage

How to build spectrum of signal? Here is simple, but detailed example of Matlab's fft() function usage. Also I showed how correctly plot discrete time signal and discrete spectrum of signal.