| This dissertation introduces new digital signal processing methods to model the distortion and tone of musical instrument amplifiers and audio signal processes such as vacuum tubes, guitar amps, distortion effects, tone circuits, equalizers, loudspeaker cabinets, microphones, compressors, and reverberant spaces. Efficient techniques to represent non-linear curves, emulate non-linear dynamical systems, and to implement convolution with large filters in real-time and with low latency are presented.;New functions to model the characteristic curves of vacuum tubes, semiconductors, and distortion circuits are described, ranging from simple forms using rational functions to more sophisticated curves based on Bezier splines. These are incorporated into non-linear differential equations used to describe the behavior of non-linear circuits, vacuum tube preamplifiers, and power amplifier stages. This dissertation introduces new numerical methods for emulating these non-linear systems in real-time that provide fast, efficient, and stable solvers for the vacuum tube and distortion models they represent.;Furthermore, many real-world continuous-time systems, and especially those required to model the subsystems of an instrument amplifier or audio signal processor such as the tone control circuits, loudspeakers, reverberation models, and other complex filters, can be approximated with finite impulse response filters. In applications where this discrete-time impulse is appreciably long and where its convolution with an input sequence must be performed in real-time without noticeable group delay, efficient low-latency block convolution methods are required. This dissertation describes various existing algorithms for fast convolution, including the direct-form FIR, overlap-save, single-FDL uniform segmentation, dual-FDL uniform segmentation, and non-uniform segmentation techniques and introduces new zero-latency variations using direct-form FIR header blocks. New algorithms for implementing the overlap-save and single-FDL methods are presented along with a cost analysis and relative performance comparison of their use in other block convolution techniques. Optimum selection of the existing block convolution techniques and their most efficient configurations for different impulse response lengths are also determined and tabulated. |
