How to create a Frequency Spectrum plot from nonlinear equations

given three nonlinear equations

dx1/dt = 3(x1+x2)

dx2/dt = x1 - (1/6)x2

dx3/dt = (1/7) + (x1 -3.25)*x3

and their correspoding initial condtion x1(0) = 0, x2(0) = 4 and x3(0) = 0, I able to obtain t,x from using ODE 45, but after that I am quiet lost how to create a frequency spectrum from using the three nonlinear equations. please help! Seems like all the output from equation are non-unifrom therefore, interpolation has to be invovled but not sure how to do it. Please help with through explanations!

Answer 1

[Pratyush]

Hello PetronasAMG,

To create a frequency spectrum from the solutions of nonlinear differential equations solved using `ode45` in MATLAB, follow these steps:

Interpolate the non-uniform output from "ode45" onto a uniform time grid.

• Use "interp1" to interpolate the solutions ("x1", "x2", "x3") onto a new uniform time grid.

Compute the Fast Fourier Transform (FFT) of the interpolated signals.

• Use "fft" to compute the FFT of each interpolated signal.
• Calculate the single-sided spectrum from the double-sided spectrum obtained from the FFT.

Plot the Frequency Spectrum to visualize the frequency content.

• Plot the magnitude of the FFT versus frequency for each signal.

This process involves interpolating the original, non-uniformly spaced solutions to create uniformly spaced data, which is then used to compute and visualize the frequency spectrum through FFT.