Plotting amplitude spectrum of a signal

i got this sygnal

tmax=0.5;

t=0:0.001:tmax;

fs=1000;

tsamp=0:1/fs:tmax;

f1 = 18;

f2 = 321.37;

y = sin(2*pi*f1*tsamp) + sin(2*pi*f2*tsamp);

figure();

plot(t, y);

grid on;

how do I plot it's amplitude spectrum?

Answer 1

[Star Strider]

Try something like this —

     tmax=0.5;
  t=0:0.001:tmax;
    fs=1000;
    tsamp=0:1/fs:tmax;
    f1 = 18;
    f2 = 321.37;
    y = sin(2*pi*f1*tsamp) + sin(2*pi*f2*tsamp);
    figure();
    plot(t, y);
    grid on;

    
    L = numel(t);
    Fn = fs/2;
    NFFT = 2^nextpow2(L);
    FTy = fft(y,NFFT)/L;
    Fv = linspace(0, 1, NFFT/2+1)*Fn;
    Iv = 1:numel(Fv);
    
    figure
    plot(Fv, abs(FTy(Iv))*2)
    grid on
    xlabel('Frequency')
    ylabel('Magnitude')

    
    FTyw = fft(y(:).*hann(L),NFFT)/L;
    
    figure
    plot(Fv, abs(FTy(Iv))*2)
    grid on
    xlabel('Frequency')
    ylabel('Magnitude')
    title('Windowed')

.

[Artyom]

thank you so very much! it looks like what i needed! could you help me a bit more, please? i just got the infromation that the amplitude spectrum should be in dB & in the range of +- half of the sampling frequency. could you modify it that way?

[Star Strider]

A two-sided Fourier transform is straightforward in MATLAB.

Calculating it with its declared length and with a power-of-2 length and a window —

     tmax=0.5;
    t=0:0.001:tmax;
    fs=1000;
    tsamp=0:1/fs:tmax;
    f1 = 18;
    f2 = 321.37;
    y = sin(2*pi*f1*tsamp) + sin(2*pi*f2*tsamp);
    figure();
    plot(t, y);
    grid on;

    
    L = numel(t);
    Fn = fs/2;
    FTy = fft(y)/L;
    Fv = linspace(-fs/2, fs/2, L);                              % Odd-Length Vector (Symmetric)
    
    figure
    plot(Fv, mag2db(abs(FTy)))
    grid on
    xlabel('Frequency')
    ylabel('Magnitude (dB)')

    
    NFFT = 2^nextpow2(L);
    FTyw = fft(y(:).*hann(L),NFFT)/L;                           % Use Power-Of-2 Length & Window
    Fv = linspace(-fs/2, fs/2-fs/NFFT, NFFT);                   % Even-Length Vector (Asymmetric)

    figure
    plot(Fv, mag2db(abs(FTyw)))
    grid on
    xlabel('Frequency')
    ylabel('Magnitude (dB)')
    title('Power-Of-2 & Windowed')

.

[Artyom]

it gives me an error in

FTyw = fft(y(:).*hann(L),NFFT)/L;

says "Undefined function 'hann' for input arguments of type 'double'."

could "hann" be replaced somehow?

[Star Strider]

The hann function is part of the Signal Processing Toolbox. Just delete that part of my code, and note that it will still be here if you need it for future reference. (My intent was to demonstrate doing a power-of-2 fft and using a window function.)

Answer 2

[Sulaymon Eshkabilov]

   tmax=0.5;
  t=0:0.001:tmax;
    fs=1000;
    tsamp=0:1/fs:tmax;
    f1 = 18;
    f2 = 321.37;
    y = sin(2*pi*f1*tsamp) + sin(2*pi*f2*tsamp);
    figure();
    plot(t, y);
    grid on;

    Y =movmedian(y, 5);  % Amplitude
    figure
    plot(t,Y)
     grid on
    xlabel('x')
    ylabel('|y(x)|')