enforce minimum phase using hilbert transform

Hello group, I have a  question regarding minimum phase system and causal
enforcement.

For a minimum phase system, the measured discrete frequency domain data
are given. To remove the measurement noise, I use the
-hilbert(log(abs(H(F))) to generate the phase of the system, and then get
time domain waveform through h(t) = IFFT(abs(H(F))* exp(j*phi(F))). I found
h(t) is not causal. 

From the text book, it says the minimum phase system is causal and
stable.
I don't understand it's not causal in my case. 

thanks a LOT and admiration to anyone able and willing to answer,

I am not sure what you mean by:

"To remove the measurement noise, I use the
-hilbert(log(abs(H(F))) to generate the phase of the system"

But have you tried using the matlab's rceps function to generate a MP
version of your signal it seems to be doing something similar to what
you have attempted)? :

http://www.mathworks.com/access/helpdesk/help/toolbox/signal/index.html?/access/helpdesk/help/toolbox/signal/rceps.html&http://www.google.com/search?hl=en&q=cepstrum+minimum+phase&aq=f&oq=