AuditoryHierarchy_DataSetAndCode/Code/Utilities/GetMomentsNoiseSignal.m

function [SigMom, NoiseMom,Kurtosis,Var] = GetMomentsNoiseSignal(Vals)

Trnum = size(Vals,2);

%% 1st order
SigMom.M1 = nanmean(nanmean(Vals,1),2);
NoiseMom.M1 = 0;

%% 2nd order

SigMom.M2 = (1/(Trnum-1)) * (Trnum * nanmean(nanmean(Vals,2).^2,1) - nanmean(nanmean(Vals.^2,1),2))';
NoiseMom.M2 = nanmean(nanmean((Vals - nanmean(Vals,2)).^2,1),2)/(1-1/Trnum);


%% Third order
% some useful intermediary values
Int1 = nanmean(nanmean(Vals,2).^3);
Int2 = nanmean(nanmean(Vals.^3,1),2);

NoiseMom.M3 = (1/(1-1/Trnum^2))*(Int2 - Int1 + (3/Trnum-3)*SigMom.M1*NoiseMom.M2);
% NoiseMom.M21 =((1+2/Trnum^2)*NoiseMom.M3 - nanmean(nanmean((Vals-nanmean(Vals,2)).^3,2),1))/3;
SigMom.M3 = Int2 - NoiseMom.M3 -3*SigMom.M1*NoiseMom.M2;

%% Fourth order
% some useful intermediary values
Int1 = nanmean(nanmean(Vals,2).^4);
Int2 = nanmean(nanmean(Vals.^4,1),2);

NoiseMom.M4 = (1/(1-1/Trnum^3))*(Int2 - Int1 + ((3*Trnum-3)*NoiseMom.M2^2)/(Trnum^3)...
    -(4-4/Trnum^2)*NoiseMom.M3*SigMom.M1 - (6-6/Trnum)*NoiseMom.M2*SigMom.M2);

SigMom.M4 = Int2 - NoiseMom.M4 - 4*NoiseMom.M3*SigMom.M1 - 6*SigMom.M2*NoiseMom.M2;

%% Kurtosis
Num = SigMom.M4 - 4*SigMom.M1*SigMom.M3 + 6*SigMom.M1^2*SigMom.M2 -3*SigMom.M1^4;
Denom = (SigMom.M2 - SigMom.M1^2)^2;

Kurtosis = Num/Denom - 3;

%% Var
 Var = nanmean(nanmean((Vals - SigMom.M1).^2,1),2) - NoiseMom.M2;

%SigMom.M2 + NoiseMom.M2-SigMom.M1^2;


end