How to plot the frequency spectrum of a signal on Matlab?

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Gabriel Borrero 2012-11-4

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    Hello everybody I have already developed a small code with a lot of help from Mathworks and the help function (in Matlab), and from some forums but I need someone to help me with my code. It's pretty much working but the spectrum's amplitude is not going according to theory. It should be half of the carrier's amplitude which in my case should be 25 volts, but Matlab's plot gives 22.51 volts which is not correct also on the sidebands I am getting 8.476 volts and it should be a quarter of the carrier's amplitude which in my case is 12.5 volts.

Here is my code:

    clear all;clc
    Fs = 200; % Sampling frequency Fs >> 2fmax & fmax = 50 Hz
    t = 0:1/Fs:7501; % length (x) = 7501
    x = 50*(1+0.75*sin(2*pi*t)).*cos(100*pi*t); % AM Signal
    xdft = (1/length(x)).*fft(x);
    freq = -100:(Fs/length(x)):100-(Fs/length(x)); %Frequency Vector
    y = abs(fftshift(xdft));
    figure(1); % Plot signals in both time and frequency domain
    subplot(211);plot(t,x);grid on;title 'Amplitude Modulated Signal';
    axis([0 5 -100 100]);xlabel 'Time (sec)';ylabel 'Amplitude (volts)';
    subplot(212);plot(freq,y);grid on;title 'AM Signal Spectrum';
    axis([-60 60 0 25]);xlabel 'Frequency (Hz)';ylabel 'Amplitude (volts)';

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Azzi Abdelmalek 2012-11-4

What is the problem with your code?

Gabriel Borrero 2012-11-4

The code is apparently working but it is not giving me the correct values in the spectrum's amplitude and I don't know how why or how to fix it, so far it is the best I could find for plotting the frequency domain of a signal.

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Gabriel Borrero 2012-11-4

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https://ww2.mathworks.cn/matlabcentral/answers/52739-how-to-plot-the-frequency-spectrum-of-a-signal-on-matlab#answer_64280

Before with my time vector wrong t = 0:1/Fs:7501; % length (x) = 7501 <http://i920.photobucket.com/albums/ad48/gabrielthemessenger/before.jpg>

After with the correct time vector t = 0:1/Fs:1-1/Fs; <http://i920.photobucket.com/albums/ad48/gabrielthemessenger/after.jpg>

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Gabriel Borrero 2012-11-21

Sorry I don't know how to undo it :(

Azzi Abdelmalek 2012-11-21

Never mind

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Azzi Abdelmalek 2012-11-4

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编辑：Azzi Abdelmalek 2012-11-4

在 MATLAB Online 中打开

The frequency of your signal is F=1 Hz, Then why t = 0:1/Fs:7501

I suggest

t = 0:1/Fs:1-1/Fs

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Azzi Abdelmalek 2012-11-5

编辑：Azzi Abdelmalek 2012-11-5

why should they be 12.5? I have also, used my code and get the same result then you

Gabriel Borrero 2012-11-5

Because the theory establishes that the amplitude of those frequency components should be half the carrier's amplitude in my case the carrier's amplitude is 50 volts so when it is transformed into the frequency domain the amplitude decreases by half on the carrier representation in the frequency domain so it should be 25 volts on the middle impulse (carrier) & one quarter of the carrier's amplitude on both the upper & lower impulses so 50/4 = 12.5 volts.

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