Theses and Dissertations at Montana State University (MSU)
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Item Assessing nonlinearity and memory extent in audio systems(Montana State University - Bozeman, College of Engineering, 2021) Hoerr, Ethan Randall; Chairperson, Graduate Committee: Robert C. MaherCreating 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.Item Multiple embodiment instructional sequence using the computer as the interfacing agent in the instruction of volume of rectangular solids(Montana State University - Bozeman, College of Education, Health & Human Development, 1989) Johnson, Ruth Mary ReglingThis study measured the effect of two multiple embodiment instructional sequences on the topic of volume of rectangular solids upon student achievement. Instructional sequences investigated were (1) the sequence with computer, (2) the same sequence without computer ; and a textbook-based sequence. Independent variables were sequence, ability level, and gender. Dependent variables were scores on post-instruction and post-retention criterion-referenced tests. Test items were divided into these categories: knowledge and comprehension, application and analysis, and total test. A pretest determined all sequence groups were equal before instruction. The four-week study was conducted in 21 southwestern Montana classrooms. Classes were randomly assigned to the sequences. Classroom teachers conducted all instruction and testing activities. Post-instruction test was administered after one week of instruction; post-retention test after three weeks of retention activities, one activity each week. Factorial analysis of scores established the following conclusion. Both multiple embodiment sequences were superior to the textbook sequence except for application and analysis post-instruction scores. The highest achievement was among high ability groups; the lowest achievement was among low ability. Males outperformed females on knowledge and comprehension questions; females outperformed males on the computer sequence; and on both tests, males and females demonstrated equal achievement on application and analysis and total test scores. Two trends were noted: (1) students in the embodiment sequence without computer produced higher scores post-instruction, but students in the computer embodiment sequence scored higher post-retention, and (2) low ability students in the computer sequence scored lower than their counterparts in the other sequences. The following recommendations were made concerning instruction of volume of rectangular solids. Carefully sequenced multiple embodiment instruction should be used. Use of the computer should be considered in embodiment instruction. Assumption that male achievement is superior to female achievement in this area should not be made. Instruction on this topic should be reinforced over time and should include multiple embodiments.Item Uncountable collections of unimodal continua(Montana State University - Bozeman, College of Letters & Science, 2000) Johanson, Paul James