hello
seems to me you're comparing apples and oranges
csd gives the cross power spectral density , not a transfer function estimate
fyi : this is the code (of an older version) of tfestimate ; in the litterature this is called the H1 estimator and the Txy transfer function uses Pxx and Pxy :
for zero extra fee you get also the coherence as you have also Pyy :
%%%%%%%%%%%%%%%%%%%%%%%
function [Txy,Cxy,f] = mytfe_and_coh(x,y,nfft,Fs,window,noverlap)
% Transfer Function and Coherence Estimate
% compute PSD and CSD
window = window(:);
n = length(x); % Number of data points
nwind = length(window); % length of window
if n < nwind % zero-pad x , y if length is less than the window length
x(nwind)=0;
y(nwind)=0;
n=nwind;
end
x = x(:); % Make sure x is a column vector
y = y(:); % Make sure y is a column vector
k = fix((n-noverlap)/(nwind-noverlap)); % Number of windows
% (k = fix(n/nwind) for noverlap=0)
index = 1:nwind;
Pxx = zeros(nfft,1);
Pyy = zeros(nfft,1);
Pxy = zeros(nfft,1);
for i=1:k
xw = window.*x(index);
yw = window.*y(index);
index = index + (nwind - noverlap);
Xx = fft(xw,nfft);
Yy = fft(yw,nfft);
Xx2 = abs(Xx).^2;
Yy2 = abs(Yy).^2;
Xy2 = Yy.*conj(Xx);
Pxx = Pxx + Xx2;
Pyy = Pyy + Yy2;
Pxy = Pxy + Xy2;
end
% Select first half
if ~any(any(imag([x y])~=0)) % if x and y are not complex
if rem(nfft,2) % nfft odd
select = [1:(nfft+1)/2];
else
select = [1:nfft/2+1]; % include DC AND Nyquist
end
Pxx = Pxx(select);
Pyy = Pyy(select);
Pxy = Pxy(select);
else
select = 1:nfft;
end
Txy = Pxy ./ Pxx; % transfer function estimate
Cxy = (abs(Pxy).^2)./(Pxx.*Pyy); % coherence function estimate
f = (select - 1)'*Fs/nfft;
end
