text: Z-HIT is a special case of the Hilbert transform and through restriction by the Kramers–Kronig relations it can be derived for one-Port-systems. The frequency-dependent relationship between impedance and phase angle can be observed in the Bode plot of an impedance spectrum. Equation (1) is obtained as a general solution of the correlation between impedance modulus and phase shift.
  Equation (1) indicates that the logarithm of the impedance () at a specific frequency  can be calculated up to a constant value of (), if the phase shift  is integrated up to the frequency point of interest , while the starting value  of the integral can be freely chosen. As an additional contribution to the calculation of , the odd-numbered derivatives of the phase shift at the point  have to be added, weighted with the factors .
  The factors  can be calculated according to equation (2), whereat  represents the  Riemann ζ-function.
  The practically applied Z-HIT approximation is obtained from equation (1) by limitation to the first derivative of the phase shift neglecting higher derivatives (equation (3)), where C represents a constant.
  The free choice of the integration boundaries in the ZHIT algorithm is a fundamental difference concerning the Kramers-Kronig relations; in ZHIT the integration boundaries are 
    and . 
  The greatest advantage of the ZHIT results from the fact, that both integration boundaries can be chosen within the measured spectrum,  and thus does not require extrapolation to frequencies 0 and , as with the Kramers-Kronig relations.