Assessing nonlinearity and memory extent in audio systems
Hoerr, Ethan Randall
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Creating digital models of existing audio devices is useful for increasing access to audio effects and for preserving audio history. In the work covered by this dissertation, we investigate 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. 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. We propose that this benchmarking method can aid a system modeler by elucidating details about a system's nonlinear behavior. We also assess 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. As a nonlinear metric of correlation between an input signal x[n] and output signal y[n], the TDMI method in MATLAB simulations accurately predicted the significant samples of delay lines, FIR moving average filters, and Schroeder all-pass filters. The TDMI method was less informative when applied to IIR low pass filters with and without an arctangent function appended to the output. Finally, we 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. In summary, we 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.