Some aspects of harmonic time series analysis

**Authors:**Human, Johannes Urbanus**Date:**2012-01-17**Subjects:**Harmonic analysis , Time-series analysis**Type:**Thesis**Identifier:**uj:1913 , http://hdl.handle.net/10210/4275**Description:**Ph.D. , Harmonic time series are often used to describe the periodic nature of a time series, for example the periodic nature of a variable star’s observed light curve. Statistical methods for determining the number of harmonic components to include in harmonic time series are limited. In this thesis a stepwise bootstrap procedure based on a F-type statistic is suggested. The performance of the stepwise procedure is compared to that of Schwartz’s Bayesian Criterion (SBC) and a procedure based on a statistic described by Siegel (1980). Harmonic series with correlated noise terms and irregularly spaced observations are also considered. Tests to detect changes in harmonic parameters are also derived in this thesis. A cumulative sum statistic to test for constant amplitude is derived. It is shown that testing for constant amplitude is equivalent to testing for constant slope in simple linear regression. We also derive a likelihood ratio statistic to test for constant amplitude. It is shown that the latter likelihood ratio statistic is asymptotically equivalent to the cumulative sum statistic. These statistics are compared to a quadratic form statistic used by Koen (2009). Likelihood ratio tests are also derived for detecting changes in the frequency or phase of harmonic time series. Graphical devices to aid in diagnostic checking are suggested.**Full Text:**

**Authors:**Human, Johannes Urbanus**Date:**2012-01-17**Subjects:**Harmonic analysis , Time-series analysis**Type:**Thesis**Identifier:**uj:1913 , http://hdl.handle.net/10210/4275**Description:**Ph.D. , Harmonic time series are often used to describe the periodic nature of a time series, for example the periodic nature of a variable star’s observed light curve. Statistical methods for determining the number of harmonic components to include in harmonic time series are limited. In this thesis a stepwise bootstrap procedure based on a F-type statistic is suggested. The performance of the stepwise procedure is compared to that of Schwartz’s Bayesian Criterion (SBC) and a procedure based on a statistic described by Siegel (1980). Harmonic series with correlated noise terms and irregularly spaced observations are also considered. Tests to detect changes in harmonic parameters are also derived in this thesis. A cumulative sum statistic to test for constant amplitude is derived. It is shown that testing for constant amplitude is equivalent to testing for constant slope in simple linear regression. We also derive a likelihood ratio statistic to test for constant amplitude. It is shown that the latter likelihood ratio statistic is asymptotically equivalent to the cumulative sum statistic. These statistics are compared to a quadratic form statistic used by Koen (2009). Likelihood ratio tests are also derived for detecting changes in the frequency or phase of harmonic time series. Graphical devices to aid in diagnostic checking are suggested.**Full Text:**

The sampling theorem based methodology for harmonics analysis

- Bokoro, P., Pretorius, J., Case, M.

**Authors:**Bokoro, P. , Pretorius, J. , Case, M.**Date:**2012**Subjects:**Sampling theorem , Line current harmonics , Thyristor converters , Harmonic analysis**Type:**Article**Identifier:**uj:6271 , http://hdl.handle.net/10210/8897**Description:**This paper investigates the validity of the sampling theorem in the analysis of supply side line current harmonics as applied to 6-pulse AC-DC thyristor converters. The common pattern of the percentage harmonic factor, for the converter characteristic harmonic current, per incremental change of the thyristor firing angle is used as the basis of the study. The RMS values of the peak amplitudes of the characteristic harmonic currents induced in the input-phase of the converter supplying a DC motor are described in terms of the sampling theorem equations and further evaluated in terms of their respective individual harmonic contributions as the thyristor firing angle is changed. The MatLab/Simulink package is also employed to simulate the forward drive speed control operation of a DC motor using the 6-pulse AC-DC thyristor converter. However the percentage harmonic factor trends observed in the sampling theorem method appear to be generally increasing which is in contradiction to the MatLab/Simulink produced trends.**Full Text:**

**Authors:**Bokoro, P. , Pretorius, J. , Case, M.**Date:**2012**Subjects:**Sampling theorem , Line current harmonics , Thyristor converters , Harmonic analysis**Type:**Article**Identifier:**uj:6271 , http://hdl.handle.net/10210/8897**Description:**This paper investigates the validity of the sampling theorem in the analysis of supply side line current harmonics as applied to 6-pulse AC-DC thyristor converters. The common pattern of the percentage harmonic factor, for the converter characteristic harmonic current, per incremental change of the thyristor firing angle is used as the basis of the study. The RMS values of the peak amplitudes of the characteristic harmonic currents induced in the input-phase of the converter supplying a DC motor are described in terms of the sampling theorem equations and further evaluated in terms of their respective individual harmonic contributions as the thyristor firing angle is changed. The MatLab/Simulink package is also employed to simulate the forward drive speed control operation of a DC motor using the 6-pulse AC-DC thyristor converter. However the percentage harmonic factor trends observed in the sampling theorem method appear to be generally increasing which is in contradiction to the MatLab/Simulink produced trends.**Full Text:**

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