HIPSR (HI-Pulsar) is a digital signal processing system for the Parkes 21-cm Multibeam Receiver that provides larger instantaneous bandwidth, increased dynamic range, and more signal processing power than the previous systems in use at Parkes. The additional computational capacity enables finer spectral resolution in wideband HI observations and real-time detection of Fast Radio Bursts during pulsar surveys. HIPSR uses a heterogeneous architecture, consisting of FPGA-based signal processing boards connected via high-speed Ethernet to high performance compute nodes. Low-level signal processing is conducted on the FPGA-based boards, and more complex signal processing routines are conducted on the GPU-based compute nodes. The development of HIPSR was driven by two main science goals: to provide large bandwidth, high-resolution spectra suitable for 21-cm stacking and intensity mapping experiments; and to upgrade the Berkeley–Parkes–Swinburne Recorder (BPSR), the signal processing system used for the High Time Resolution Universe (HTRU) Survey and the Survey for Pulsars and Extragalactic Radio Bursts (SUPERB).