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Dear SPM'ers,

I want to plot the power spectrum of the estimated global AR(1) + white 
noise model that is used in SPM.

I first create the residual forming matrix by  I - S*X * pinv(S*X), 
where X is the design matrix and S is the filtering matrix

residual_forming_matrix = eye(number_of_timepoints) - SPM.xX.xKXs.X * 
SPM.xX.pKX;

I then multiply this matrix with the non-sphericity estimate, to obtain 
the correlation matrix

correlation_matrix = residual_forming_matrix * SPM.xVi.V;

As this matrix has a Toeplitz structure, I can obtain the auto 
correlation function as the first row (or column) of this matrix

correlation_function = correlation_matrix(:,1);

Finally I calculate the spectrum by using a Fourier transform

abs(fftshift(fft(correlation_function)))



Can anyone tell me if this is correct?


/Anders

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Anders Eklund
Phd student

Medical Informatics,  Department of Biomedical Engineering
CMIV, Center for Medical Image Science and Visualization

Tel:  +46 73 6003790        mail: [log in to unmask]
Fax:  +46 13 101902         web: http://www.wanderineconsulting.com/
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