Doing Fourier transform (FFT) of the output of an ode45 solution and subsequent plotting in the frequency domain.

I want to do the FFT of the output of an ode45 solution and then plot it in the frequency domain.

The solution of the ODE is sinusoidal with specific frequency but upon transforming (FFT) the solution and then plotting in the frequency domain, I am getting spikes at different frequencies. The issue seems to be with the choice of sampling frequency for FFT. Please suggest.

Answer 1

[Star Strider]

The fft function requires that the time domain signal be samoled at regular intervals. The numerical dddifferential equation integrators will produce a time vector with irregular intervals if you only give it a ‘tspan’ argument with 2 elements, however it will produce results at uniform spacing if ‘tspan’ is a vector of more than two elements. Taht can then be used with fft.

de = @(t,x) [x(1);  1./(5 - x(1))];
ic = [1 1];
tspan = [0 5];
[T,Y] = ode45(de, tspan, ic);

figure
plot(T,Y,'.-')
grid

tspan = linspace(0, 5, 50);
[T,Y] = ode45(de, tspan, ic);

figure
plot(T,Y,'.-')
grid

.

[Gaurab]

Thanks!!

[Star Strider]

My pleasure!

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