A fast digital signal processing (DSP) system is described that can perform real-time emulation of a wide variety of linear audio-bandwidth systems and networks, such as reverberant spaces, musical instrument bodies and very high order filter networks. The hardware design is based upon a Motorola DSP56309 operating at 110 million multiplication-accumulations per second and a dual-channel 24 bit codec with a maximum sampling frequency of 192 kHz. High level software has been developed to express complex vector frequency responses as both infinite impulse response (IIR) and finite impulse response (FIR) coefficients, in a form suitable for real-time convolution by the firmware installed in the DSP system memory. An algorithm has also been devised to express IIR filters as equivalent FIR structures, thereby obviating the potential instabilities associated with recursive equations and negating the traditional deficiencies of FIR filters respecting equivalent analogue designs. The speed and dynamic range of the system is such that, when sampling at 48 kHz, the frequency response can be specified to a spectral precision of 22 Hz; when sampling at 10 kHz, this resolution increases to 0.9 Hz. Moreover, it is also possible to control the phase of any frequency band with a theoretical precision of 10-5 degrees in all cases. The system has been applied in the study of analogue filter networks, real-time Hilbert transformation, phase-shift systems and musical instrument body emulation, where it is providing valuable new insights into the understanding of psychoacoustic mechanisms.