There is a constant need for the increase of transfer rate in wireless communication systems. Therefore, these systems must be continuously improved. This is particularly true for radio subsystems, which are often bottlenecks of entire communication chains. Software defined radio has been recognized as crucial technology for their development. Following this trend, the proposed project considers the improvement of existing and the development of new methods for the design of signal processing systems for software defined radio. In particular, the project is focused on multirate systems, conventional and spatial filters, as well as on the systems for optimal utilization of spectrum in ultra-wideband radio. Efficient signal processing and efficient implementation are required of all these systems. To increase the efficiency, the research will utilize time- and frequency-domain synthesis, compressed sensing, polynomial sharpening, optimization and various other analytical and numerical techniques. As project results, new methods are expected for the design of systems for multirate signal processing and for the design of systems with sparse coefficients such as selective filters, differentiators, integrators and systems with constant and variable delay. Furthermore, a contribution is expected in the design of antenna arrays that enable robust beamforming and provide nearly independent control of beamwidth, directivity, sidelobe level, and dynamic range ratio. Finally, new methods will be developed for the synthesis of energy- and spectral-efficient pulses for ultra-wideband communications. The resulting methods will be directly applicable in the development of communication systems. Furthermore, the involvement of doctoral students will ensure a high educational impact and the transfer of knowledge to the industrial environment. All of these factors are important because in recent years the communication sector in Croatia develops intensively.