Is the unit of Cxy from cpsd in decibel?

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!

Answer 1

[Wayne King]

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);

[Wayne King]

By the way, another common convention for "dB" is the log10 of the power measures. 10*log10(abs(Pxy).^2) or 20*log10(abs(Pxy))

[Kay]

so 20*log10(abs(Pxy)) gives me the values in dB? not dB/hz?

Also, if I want to plot the phase of Pxy, is that simply do:

phase = angle(Pxy);

?

thanks a lot!!

Kay

[Wayne King]

yes, angle(Pxy) gives you the phase. The difference between 10*log10() and 20*log10() is the difference between magnitude and magnitude squared, they are both in dB per unit frequency.

[Kay]

is dB same as dB/Hz?

if not, how do I get rid it?

Answer 2

[Kay]

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]

offset after what result?

Answer 3

[Giandomenico]

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?