Analysis of the dielectric permittivity spectrum represents an invaluable tool for inferring soil physical properties of interest, such as the volumetric water content, the volume fraction of bound water, and the specific surface area. While Time Domain Spectroscopy (TDS) measurements are routinely performed in disciplines including physical chemistry, material science and medical diagnostics, this technique is underutilized in the soil sciences. The primary reason for this is that the experimental setup commonly used in soil science differs considerably from that used in fields where the fundamentals of TDS have been developed and applications brought to maturity. As a consequence, the working equations and theoretical results demonstrated as valid for other fields are in many cases not directly applicable in soil science. In addition, the electrical model for the cable-probe system involves four unknown parameters to be determined through calibration. Due to approximations in the model and to lack of precise standard materials, determination of the calibration parameters is particularly uncertain and tedious. Based on the Cole impedance analysis, we developed a general working equation for spectroscopy measurements that is suitable for soil science applications. We found that the experimental setup is successfully characterized by only two complex parameters. In particular, we show that TDS measurements can be performed without prior determination of the probe's electric length, which had represented a major drawback of the technique. This result not only simplifies the calibration procedures, but substantially improves the accuracy of the measurements. Based on impedance spectroscopy analysis of TDR signals we were able to measure for the first time the permittivity spectrum of materials with very good accuracy over a wide frequency range using conventional TDR instruments.