Pwelch only returns a single value?

I am trying to use the pwelch method in order to calculate the coherence magnitude squared between two signals with confidence intervals. However, the pwelch function only returns a single value. What am I doing wrong?

I also attached the variables I use in my code.

My code:

%calculate pwelch

 fs=1/i_ph1.spacing_l;
    
    [pwelch_1,f1,pxx1]=pwelch(i_ph1.l,hanning(length(i_ph1.l)),(length(i_ph1.l))/2,fs,'ConfidenceLevel',0.95);
    [pwelch_2,f2,pxx2]=pwelch(i_ph2.l,hanning(length(i_ph2.l)),(length(i_ph2.l))/2,fs,'ConfidenceLevel',0.95);
    [pwelch_3,f3,pxx3]=pwelch(i_ph3.l,hanning(length(i_ph3.l)),(length(i_ph3.l))/2,fs,'ConfidenceLevel',0.95);
    [pwelch_12,f12,pxx12]=pwelch(xcorr(i_ph1.l,i_ph2.l),hanning(length(i_ph1.l)),(length(i_ph1.l))/2,fs,'ConfidenceLevel',0.95);
    [pwelch_23,f23,pxx23]=pwelch(xcorr(i_ph2.l,i_ph3.l),hanning(length(i_ph2.l)),(length(i_ph2.l))/2,fs,'ConfidenceLevel',0.95);
    [pwelch_31,f13,pxx13]=pwelch(xcorr(i_ph3.l,i_ph1.l),hanning(length(i_ph3.l)),(length(i_ph3.l))/2,fs,'ConfidenceLevel',0.95);
    %calculate CMS
    %Pxy^2/Pxx*Pyy
    CMS12=(pwelch_12).^2./(pwelch_1.*pwelch_2);
    CMS23=(pwelch_23).^2./(pwelch_2.*pwelch_3);
    CMS13=(pwelch_31).^2./(pwelch_3.*pwelch_1);
    %calculate CMS of conf intervals
    CMS_c13=(pxx12).^2./(pxx1.*pxx2);
    CMS_c23=(pxx23).^2./(pxx2.*pxx3);
    CMS_c13=(pxx13).^2./(pxx1.*pxx3);
    

[Mathieu NOE]

hello

have you tried mscohere ?

help mscohere

mscohere Magnitude Squared Coherence Estimate.

Cxy = mscohere(X,Y) estimates the magnitude squared coherence estimate

of the system with input X and output Y using Welch's averaged,

modified periodogram method. Coherence is a function of frequency with

values between 0 and 1 that indicate how well the input X corresponds

to the output Y at each frequency. The magnitude squared coherence,

Cxy, is given by Cxy = (abs(Pxy).^2)./(Pxx.*Pyy) where Pxx and Pyy are

the power spectral density (PSD) estimate of X and Y, respectively; and

Pxy is the Cross-PSD (CPSD) estimate of X and Y. See "help pwelch" and

"help cpsd" for complete details.

Answer 1

[Shushant]

Hi Shayma Al Ali,

I understand that you are using the "pwelch" function to calculate the coherence magnitude squared between two signals with confidence intervals. But the function is only returning a single value. This is because the "pwelch" function is expecting "fs" to be the fifth argument.

To solve this issue, specify the fourth argument as empty "[]". Refer to the following code snippet for the modified function call:

[pwelch_1,f1,pxx1]=pwelch(i_ph1.l,hanning(length(i_ph1.l)),(length(i_ph1.l))/2,[],fs,'ConfidenceLevel',0.95);

Refer to the following documentation for information on why the fourth argument should be empty-

https://in.mathworks.com/help/signal/ref/pwelch.html

I hope this helped in solving the issue you were facing.

Thank you,

Shushant