We developed a user-friendly software application for generating synthetic Time Domain Reflectometry (TDR) waveforms. The waveform results from the convolution of the incident voltage with a response function characterizing the TDR setup, including the feeding line - probe system and the permittivity of the sampled material. We conducted a theoretical investigation on the convolution of discrete signals, and reviewed different strategies for correcting the associated truncation errors. We found that the commonly used Nicolson ramp method performed poorly for convolution processes. Errors resulting from the product of the transfer and input functions in the frequency domain, a phenomenon known as circular convolution, were virtually eliminated by the zero-padding technique. Moreover, sophisticated modeling of the feeding line and probe which takes into account frequency dependent losses such as those resulting from the skin effect ensures very accurate reproduction of the waveforms. The software features a graphical user interface. Users can select cable length and cable type (from among the most commonly used), as well as the probe geometry. The sample material can be chosen from a library including many common solvents. Alternatively, the user can define the sample's permittivity manually by entering the parameters of the general Havriliak-Negami model for electrolyte solutions, or the Hanai model for three-phase composite materials which is generally adopted to describe soil permittivity. The model also allows users to account for Maxwell-Wagner effects and the temperature dependence of soil permittivity. Examples of the many practical software applications include optimal design of probes for specific purposes, and evaluation of the effective TDR frequency range under different measurement scenarios.