# Plotting DFT in dB

I'm having a little trouble plotting the DFT of a signal in dB. I can get the picture up nicely when using the magnitude but when I try converting the magnitude to decibels it all goes south. I've been using this for help: http://dadorran.wordpress.com/2014/02/20/plotting-frequency-spectrum-using-matlab/

Here is the code I'm running: (y is the signal obtained from a .mat file and L is the length of the signal)

Y = fft(y);
MAG = abs(Y);
MAGshift = abs(fftshift(Y));
bin_vals = [0:L-1];
L2 = L/2;
f = Fs*(bin_vals - L2)/L;

figure(1);
plot(f,MAGshift);
axis([-1000 1000 0 45000]);
grid on;


With this I managed to get this lovely picture: But when I convert the magnitude to decibels with mag2db(MAG) or 10*log10(MAG) and plot it, it does not look anything like this. Any help?

• "it does not look anything like this" It's not supposed to. What does it look like and what do you think it should look like? – endolith Oct 22 '14 at 14:01

I would suggest you to normalize the amplitude by the maximum if you don't know the exact reference or scaling:

MAG_dB = 20*log10(MAG/max(MAG));
plot(MAG_dB);


This will yield a logarithmic plot normamalised to 0 dBFS.

Small example for two sinusoids with difference in amplitude of 3dB is below:

clc, clear, close

fs = 1000;
t = (0:1/fs:10-1/fs);
N = length(t)
% Two sinusoids, second one (@200Hz) has amplitude of -3dB.
s = sin(2*pi*100*t) + 1/sqrt(2)*sin(2*pi*200*t);
s = hamming(N)'.*s;

X = abs(fft(s))/N;
X_db = 20*log10(X/max(X));

plot(X_db)
grid on • Thanks for your comment, I have attached a picture of how that looks. Doesn't look quite right to me. i.imgur.com/NFnQctF.png – dingari Oct 22 '14 at 8:49
• @user2750354: It looks perfectly OK for me. Answer updated. – jojek Oct 22 '14 at 9:11
• Ok thank you, I think I'm starting to get a better understanding of the plot I got. In the assignment there is a questing about a "significant drop in energy" above a certain frequency. That would be at the point where it drops down to ca. -40dB, right? (in the picture linked in previous comment) – dingari Oct 22 '14 at 14:18
• @user2750354: I believe that there are two correct answers. One you mentioned above (centered around 0 Hz), and a second one around 15000 Hz. – jojek Oct 22 '14 at 14:29
• Ok thanks :) I'm wondering what the effective bandwidth of the signal would be. The power drops to about -40dB at 500Hz, so would the effective bandwidth be 1000Hz? – dingari Oct 22 '14 at 15:09