MATLAB: How to plot the frequency spectrum of a signal on Matlab

amamplitudecarrierdomainfourierfrequencyintelligenceModulationsamplingsignalspectrumvolts

    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)';

Best Answer

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>

Related Solutions

MATLAB: FFT of vibration data

     Fs = 800; % sampling rate of 1000 Hz
     t = 0:1/Fs:1-1/Fs;
     x = ad2;
     xdft = fft(x);
     xdft = xdft(1:length(x)/2+1);
     DF = Fs/length(x); % frequency increment
     freqvec = 0:DF:Fs/2;
     plot(freqvec,abs(xdft))

I hope this can work

MATLAB: Specter of a square signal(10Khz) at 10MHz frequency

hello

there is a much faster method to generate a square signal (using square )

see demo below for signal generation and fft analysis

NB your sampling freq is 100 kHz in the code, not 10 MHz as stated in the post

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% dummy data
Fs = 100e3;     % sampling freq
f0 = 10e3;     % signal freq
duration = 1;   % signal duration (s)
samples = Fs*duration;
t = (0:samples-1)*1/Fs;
% signal = square(2*pi*f0*t); % neg / pos symetrical square wave ( -1 / +1)
signal = 0.5*(square(2*pi*f0*t)+1); % 0 / pos  square wave ( 0 / +1)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 10000;    % 
Overlap = 0.75;
w = hanning(NFFT);     % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display : averaged FFT spectrum 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[freq,fft_spectrum] = myfft_peak(signal, Fs, NFFT, Overlap);
sensor_spectrum_dB = 20*log10(fft_spectrum);% convert to dB scale (ref = 1)
figure(1),plot(freq,sensor_spectrum_dB,'b');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(' dB')
text(locs+.02,pks,num2str(freq(locs)))
function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer overlap % (between 0 and 0.95)
signal = signal(:);
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,1);
    s_tmp((1:samples)) = signal;
    signal = s_tmp;
    samples = nfft;
end
% window : hanning
window = hanning(nfft);
window = window(:);
%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows
    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft)).*window;
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling
% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select);
freq_vector = (select - 1)*Fs/nfft;
end

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