In the design of systems with minimum time-domain distortion, requirements can be specified in the frequency or in the time domain. The frequency domain approach is common since the design procedures are simpler. On the other hand, better results are expected using the time-domain synthesis. In that case, an appropriate model of system's input signal should be chosen. The requirements set on the system are usually given within some finite band of interest. In this thesis, the frequency-selective model of the input signal is proposed. The model is based on the zero-phase sinc pulse. This pulse uniformly excites the system at all frequencies within the prescribed band. By using the response to sinc pulse, new measures of time-domain distortion are defined, which are based on the symmetry and on the maximum of the response. These measures are suitable for optimization based design, which is used to obtain new classes of systems ensuring minimum distortion of time-domain response. Several design examples are given, including the design of lowpass and bandpass equalizers, constant-delay systems, and Hilbert transformers. Furthermore, the time-domain synthesis of systems having a desired impulse response is also considered. An efficient and robust method for the design of such systems is described. The method involves the iterative procedure based on the second-order cone programming. The features of the method are illustrated through the design of wavelet filters.