How can I transform between Time-Domain and Frequency-Domain?

Hi,

I encounter the problem of transforming a shape from the time domain to the frequency domain.

I used the following commands to convert Fourier.

n1=8;

n2=72;

nt=25501;

dt=1.176470588235294e-13;

F=zeros(n1+n2+2,nt);

F1=F(n1+n2,:);

F2 = fftshift(fft(F1));

f=linspace(-10,10,length(F2));

figure(1);

plot(f, 10*log10(abs(F2)))

Please do not doubt the values entered such as 'nt' and 'dt' because all the shapes obtained in the time domain are correct and the only problem is in converting the frequency.

Let me know please.

Thank you.

[mohammad heydari]

Does anyone have an opinion?

Answer 1

[TED MOSBY]

Hi Mohammad,

To transform a shape from the time domain to the frequency domain using the Fourier Transform in MATLAB, it seems like you're already on the right track.

Signal Initialization: Instead of initializing F to zeros, I replaced it with a random signal for demonstration. Make sure F1 contains the actual shape data you want to analyze.

Frequency Vector Calculation: The frequency vector f is derived from the sampling frequency, which is computed as Fs = 1 / dt. This provides the correct scaling for the frequency axis.

FFT Handling: The fft function is still used as you had it, but with the proper initialization for F1.

I adjusted your code with the above modifications:

% Parameters 
n1 = 8;              
n2 = 72;            
nt = 25501;          
dt = 1.176470588235294e-13;  

% Initialize the time-domain signal (example: a random signal) 
F = rand(n1 + n2 + 2, nt); 
F1 = F(n1 + n2, :);       

% Compute the Fourier Transform 
F2 = fftshift(fft(F1));   

% Frequency vector calculation 
Fs = 1 / dt;                           % Sampling frequency 
f = linspace(-Fs/2, Fs/2, length(F2)); % Frequency vector 

% Plotting the result 
figure(1); 
plot(f, 10 * log10(abs(F2))); % Plot in dB scale 
xlabel('Frequency (Hz)'); 
ylabel('Magnitude (dB)'); 
title('Frequency Domain Representation'); 
grid on; 

The output should look like this:

Hope this helps!