In addition to the reconstruction of the impedance from the phase shift, the reverse approach is also possible. However, the herein presented procedure possesses several advantages:
*  When calculating the phase shift from the impedance, a function of the angular frequency &omega; comes into play which is more difficult to determine compared to the constant C in equation (3).
* Generally, the phase shift is more stable than the impedance. This is based on the fact that for impedance elements (more precisely: Constant phase element, CPE ) the property "phase shift" remains constant even if the value of the impedance drastically changes. Such Constant Phase-elements are the typical electronic elements, among others such as the electrical resistor, capacitor and coil. For illustration, Figure 2 shows the impedance spectrum of an NTC resistor heated during the measurement (starting between 1 kHz and 10 kHz down to lower frequencies). It can clearly be seen that the value of the impedance (red curve) changes with temperature, while the phase shift (blue curve) remains constant. In other words, "a resistor remains a resistor".
* The reconstruction of the impedance from the phase shift further restores the "inner (= complex)" relationship between these two quantities. This relationship is lost by the independent construction of the supporting point splines for impedance and phase (Figure 1). Depending on the system under investigation, this restored correlation - even in the absence of artifacts - can lead to an improved evaluation of the spectra. In such cases, the gain in accuracy due to the reconstruction of the complex impedance outweighs the approximation error according to equation (3), which results from the neglection of the higher derivatives.