This paper presents the design and implementation of three System-on-Chip (SoC) cores, which implement the Digital Signal Processing (DSP) functions: Finite Impulse Response (FIR) filter, Infinite Impulse Response (IIR) filter and Fast Fourier Transform (FFT). The FIR-filter core is based on the symmetrical realization form, the IIRfilter core is based on the Second Order Sections (SOS) architecture and the FFT core is based on the Radix 22 Single Delay Feedback (R22SDF) architecture. The three cores are compatible with the Wishbone SoC bus, and they were described using generic and structural VHDL. In-system hardware verification was performed by using an OpenRisc-based SoC synthesized on an Altera FPGA. Tests showed that the designed DSP cores are suitable for building SoC based on the OpenRisc processor and the Wishbone bus.