This study assesses nonlinearity and memory extent in audio systems.
In this dissertation, the researcher investigated the use of Volterra series modeling to assess the degree of nonlinearity of a system and time-delayed mutual information (TDMI) to estimate the length of the recovered impulse response. The study demonstrated that Volterra series models are useful for assessing the degree of nonlinearity of a system and that time-delayed mutual information can inform which samples of a recovered impulse are significant. Both of these insights can aid in deciding how many Volterra series kernels and how much kernel memory to include when creating a black box system model. Creating digital models of existing audio devices is useful for increasing access to audio effects and for preserving audio history. Using an arctangent function as an example system, comparing empirically generated Volterra series models containing anywhere from first- to fourth-order system kernels revealed that including the odd-ordered first and third kernels yielded the best-performing model. This benchmarking method can aid a system modeler by elucidating details about a system's nonlinear behavior. The author also assessed the utility of time-delayed mutual information (TDMI) as a method for revealing which samples of a recovered impulse response of a nonlinear system are significant. The researcher applied the TDMI approach to a real-world audio device, a distortion effects pedal designed for electric guitar players. In the presence of increasing nonlinear distortion, the calculated TDMI curve took the shape of a pronounced peak starting at T = 0 samples delay between x[n] and y[n], with T increasing as the distortion increased. A similar phenomenon was observed when lowering the pedal's low-pass filter cutoff frequency from 36.7 kHz to 620 Hz; in the 620 Hz test, the TDMI peak was significantly lower than the other test cases and featured a more gradual decay to the estimator bias noise floor.