# FFT in dB scale

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Alexander Voznesensky on 23 Jan 2017
Hi everybody! I'm trying to use dB scale in FFT. I've found the example http://www.dsplib.ru/content/winex/winex.html
I'm trying to get the same results in MATLAB. But I can't. I have different amplitude levels. What's wrong? So, I do:
Fs=1000;
T=1/Fs;
N=1024;
t=(0:N-1)*T;
f=(0:Fs/(N-1):Fs);
A0=1;
A1=0.003;
A2=10e-4;
f0=220;
f1=240;
f2=230;
s=A0*cos(2*pi*f0*t)+A1*cos(2*pi*f1*t)+A2*cos(2*pi*f2*t);
plot(f,mag2db(abs(fft(s))));

David Goodmanson on 24 Jan 2017
hi Alexander I assume you are looking for a couple of peaks at -6 dB. Otherwise this answer will not be of help. But to get -6 dB you need to divide the fft result by N before taking mag2dB. Before getting into that, I believe your frequency grid with the factor of N-1 is not quite right. It should have a factor of N and should not end at Fs:
f = (0:N-1)*Fs/N;
That change only scales the frequency axis though, and puts the peaks in the right spot. It does not affect the peak value. You will still not get -6 dB (right now it's more like -7) because f0 = 220 does not represent an exact periodic frequency to the fft. To get a sharp peak at -6 dB, the frequency must be a multiple of Fs/N = 1000/1024. You could replace 220 by 225*1000/1024 which is pretty close, but I think the best way is to just use N = 1000. The fft is blazingly fast anyway, so unless you are in some production situation doing a ten million of these, N = 2^n is not really necessary.
Alexander Voznesensky on 22 Feb 2017
"Also, you have A2 = 10e-4 not 1e-4, so -60 dB."
Yes, it's my mistake. Now it's all right! Thank you very much!