MATLAB frequency magnitude spectrum

Question

I am using the following code to generate four sine waves using a sampling rate of 8000.

   Fs = 8000;                       % samples per second
   Ts = 1/Fs;                       % seconds per sample
   t = 0: Ts: 3;                    % Start signals at 0sec and stop after 3sec

   % Sine wave x1[n]:
   Fc = 320;                       
   x1 = sin(2*pi*Fc*t);

   % Sine wave x2[n]:
   Fc = 760;                     
   x2 = sin(2*pi*Fc*t);

   % Sine wave x3[n]:
   Fc = 1280;                       
   x3 = sin(2*pi*Fc*t);

   % Sine wave x4[n]:
   Fc = 2000;                     
   x4 = sin(2*pi*Fc*t);

   x_comp = x1 + x2 + x3 + x4;

Now I need to plot the frequency magnitude spectrum of the composite signal (x_comp) in dB. How can I achieve this please?

I used the code below but the plot is not making sense.

   x_comp = x1 + x2 + x3 + x4;

   x_comp_mag = abs(fft(x_comp)); 

Answer 1

You might be seeing the FFT coefficients shifted towards the extremes with your code. Try using fftshift() as shown below,

N=2^(nextpow2(length(x_comp)));

x_comp_mag = abs(fftshift(fft(x_comp,N)));

f = linspace(-Fs/2,Fs/2,N); % for double sided spectrum

plot(f,x_comp_mag);

Answer 2

try changing the number of samples from t = 0: Ts: 3; to t = 0: Ts: 3-Ts;

you then have a frequency resolution of 1/3 (8000/24000), which is divisible by all the chosen frequencies in your sinusoidal signal. Also does it need to be in dB ? (is abs(fft(x)) enough). some values after fft will be very small (virtually zero), but will ruin your plot if plotting log. you can round to remove the very small values, then log plot.

Answer 3

Please add the following lines to your program to get what you want...

L=length(x_comp_mag);
f=(0:(L-1))*(Fs/L); % Frequency in Hz.
figure,plot(f,20*log10(x_comp_mag));
xlabel('Frequency in Hz');
axis([0 4000 -80 100])

I got the following plot after adding these lines to your program. Is this what you want?