# Is the unit of Cxy from cpsd in decibel?

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Kay on 20 Oct 2011
Hi,
I want to use the Signal Processing Toolbox to compute the Cross spectrum gain and phase for my sequences X and Y. I wondered the Cxy that cpsd gives me is in the units of dB? I saw the example and it says the unit is dB/rad/freq, how can I convert it to dB?
Thank you so much!

Wayne King on 20 Oct 2011
Hi, no, the output is the cross spectrum, it is complex-valued. If you want the output in db. Use
10*log10(abs(Pxy));
For example:
Fs = 1000;
t = 0:1/Fs:.296;
x = cos(2*pi*t*200)+randn(size(t));
y = cos(2*pi*t*100)+randn(size(t));
[Pxy,F] = cpsd(x,y,[],[],[],Fs);
plot(F,10*log10(abs(Pxy))); grid on;
% compare to
figure;
cpsd(x,y,[],[],[],Fs);
Kay on 20 Oct 2011
is dB same as dB/Hz?
if not, how do I get rid it?

Kay on 1 Dec 2011
I'm getting some offset of the result after cpsd, do you know if the algorithm of the cpsd would give me a larger set of numbers as a result?
thanks, Kay
Wayne King on 1 Dec 2011
offset after what result?

Giandomenico on 31 Jan 2013
Edited: Giandomenico on 31 Jan 2013
I have a problem with cpsd amplitude. I generate a 20s signal with two harmonic components at 5 and 10Hz, both with an amplitude of 10, then I perform the cpsd I have the two components at the right frequencies, but both with an amplitude of 1000??? it should be 100, right?
fs=512; % sampling frequency
L=10240; % samples
t=(0:L-1)'/fs;
x=10*sin(2*pi*10*t)+10*sin(2*pi*5*t);
[Gxx, f]=cpsd(x,x,rectwin(L),0,L,fs);
plot(f,abs(Gxx),'.r')
Where I am wrong?