Instantaneous frequency calculation with Stockwell Transform code

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I calculate a signal with stockwell transform and want to get the instantaneous frequency of it.
so I write a code to calculate the Derivative of ST .
BUT it seems wrong,I change the gauss window of the stran fuction.
W=2*pi*repmat(f,nhaf,1).*repmat(invfk,1,N);
dW=2*pi*repmat(invfk,1,N);
G=exp((-W.^2)/2);
G=(-W.*dW).*G;
why it is wrong?AND how can I rewrite?

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