Before embarking on this project, Kathleen Cao wasn’t certain about what to pursue in graduate school. Now that’s clearer, after immersing herself in chemistry research with Professor Shaka. Kathleen advises others who have an interest in research not to hesitate in getting started, explaining that professors and other students provide all the necessary guidance and training on projects. In May 2002, she presented her findings at the UCI Undergraduate Research Symposium. She plans to attend graduate school in physical chemistry and hopes to continue research in NMR spectroscopy, a topic that now fascinates her. When Kathleen is not in the lab, she enjoys reading and tutoring high school students.

Two parametric fitting methods for spectrum analysis, the filter diagonalization method (FDM) and decimated signal diagonalization (DSD) method, are compared for processing one-dimensional nuclear magnetic resonance (NMR) spectroscopy time signals. These methods are alternatives to the discrete Fourier transform (DFT) for processing time domain data for NMR. FDM and DSD use pure linear algebra to diagonalize small matrices generated from an NMR time signal in order to extract the inherent spectral parameters, the characteristic frequencies and amplitudes. These techniques have advantages over DFT because they can use smaller data sets and the resolution is not restricted by the Fourier transform time-frequency uncertainty principle. The main difference between FDM and DSD is the method of generating small matrices from a single long signal; FDM filters basis functions whereas DSD filters the time signal. This comparative study shows that the development of DSD is not yet at the level of FDM, particularly for one-dimensional NMR data processing.

Athan J. Shaka School of Physical Sciences

There has never been any acceptable alternative to Fourier transform for frequency analysis of the time-dependent signal obtained in nuclear magnetic resonance. Kathleen Cao’s work on alternative linear algebraic methods of making the connection between the time and frequency domains shows why this is so. Two very closely related approaches, both of which may seem to be equivalent on paper, give markedly different results. The decimated signal diagonalization method (DSD) is obtained by first “decimating” or reducing the signal size and then extracting frequencies. The filter diagonalization method (FDM) is obtained by constructing a filtered local frequency-domain signal matrix, and then diagonalizing. Rather surprisingly, the latter is far more effective, and now, based on Kathleen’s careful investigation, we know exactly why. Making a discovery can be one of the most exciting events in one’s life, therefore, it is very important for undergraduates to conduct research and get a taste of the unknown.