All discrete function representations become exponential in size in the worst case. Binary decision diagrams have become a common method of representing discrete functions in computer-aided design applications. For many functions, binary decision diagrams do provide compact representations. This work presents a way to represent large decision diagrams as multiple smaller partial binary decision diagrams. In the Boolean domain, each truth table entry consisting of a Boolean value only provides local information about a function at that point in the Boolean space. Partial binary decision diagrams thus result in the loss of information for a portion of the Boolean space. If the function were represented in the spectral domain however, each integer-valued coefficient would contain some global information about the function. This work also explores spectral representations of discrete functions, including the implementation of a method for transforming circuits from netlist representations directly into spectral decision diagrams.

Estuaries are vital environmental and economic resources, providing habitat for thousands of species, absorbing runoff, and supporting recreation and commerce. Yet, despite their importance, estuaries are threatened by human activities. Empirical Orthogonal Function (EOF) analysis and Cross Spectral techniques were used in the analysis and prediction of estuarine morphology. The estuaries selected for study were Suisun Bay, CA and Mobile Bay, AL. It was found that EOF is an effective and efficient technique to analyze morphology, a coupling with cross spectral methods such as Fourier Transformation (FFT) resulted in determination of forcing functions responsible for imparting variance to the bathymetry. In both the estuaries it was found that the first two eigenvalues represented almost 80% of the morphological/bathymetric dataset. The second eigenfunction was found to be closely dependent on the freshwater inflows to the estuaries. EOF analysis on Suisun Bay revealed that the bay is depositional particularly in the shallow bays of Honker and Grizzly, whereas the main channels as well as Carquinez Straits maintained their depths throughout the period studied. Utilizing a Cross spectral technique, Amplitude Response Function (ARF), temporal eigenfunctions for the bay were determined for year 2100. The temporal eigenfunctions were predicted for cases where river inflows to the bay were varied by 1 standard deviation unit. These predicted eigenfunction values combined with the eigenvalues resulted in the recovery of predicted depths for year 2100. It was found that Suisun Bay remains depositional through the year 2100 and maintains depths in the main channels as well as Carquinez Straits. This depositional behavior results in the decrease of bay volume to almost 40% of the volume in 1989. EOF analysis on Mobile Bay revealed that the bay is predominantly depositional except in the navigation channel and the shoreline of the Bay. The navigation channel maintaining it depth is attributed to the regular dredging carried to facilitate shipping. The second temporal eigenfunction showed a close correlation with river inflows as in the case of Suisun Bay. However, a cross correlation performed on the second temporal eigenfunction and inflows revealed that the response of the eigenfunction is perturbed by almost 9 years, as opposed to 6 to 9 years for Suisun Bay. An ARF on the temporal eigenfunctions combined with a reverse EOF resulted in the formation of bathymetric datasets for the year 2100 for inflows variation of 1 standard deviation. It was revealed that increasing the flows results in an increase of bay volume by approximately 30% and a decrease in flows results in a loss of volume by approximately 20%.