Graph spectra and modal dynamics of oscillatory networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2003.Includes bibliographical references (leaves 186-191).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Our research focuses on developing design-oriented analytical tools that enable us to better understand how a network comprising dynamic and static elements behaves when it is set in oscillatory motion, and how the interconnection topology relates to the spectral properties of the system. Such oscillatory networks are ubiquitous, extending from miniature electronic circuits to large-scale power networks. We tap into the rich mathematical literature on graph spectra, and develop theoretical extensions applicable to networks containing nodes that have finite nonnegative weights-including nodes of zero weight, which occur naturally in the context of power networks. We develop new spectral graph-theoretic results spawned by our engineering interests, including generalizations (to node-weighted graphs) of various structure-based eigenvalue bounds. The central results of this thesis concern the phenomenon of dynamic coherency, in which clusters of vertices move in unison relative to each other. Our research exposes the relation between coherency and network structure and parameters. We study both approximate and exact dynamic coherency. Our new understanding of coherency leads to a number of results. We expose a conceptual link between theoretical coherency and the confinement of an oscillatory mode to a node cluster. We show how the eigenvalues of a coherent graph relate to those of its constituent clusters.(cont.) We use our eigenvalue expressions to devise a novel graph design algorithm; given a set of vertices (of finite positive weight) and a desired set of eigenvalues, we construct a graph that meets the specifications. Our novel graph design algorithm has two interesting corollaries: the graph eigenvectors have regions of support that monotonically decrease toward faster modes, and we can construct graphs that exactly meet our generalized eigenvalue bounds. It is our hope that the results of this thesis will contribute to a better understanding of the links between structure and dynamics in oscillatory networks.by Babak Ayazifar.Ph.D

Self-Contained Jupyter Notebook Labs Promote Scalable Signal Processing Education

[EN] Our upper-division course in Signals and Systems at UC Berkeley comprises primarily sophomore and junior undergraduates, and assumes only a basic background in Electrical Engineering and Computer Science. We’ve introduced Jupyter Notebook Python labs to complement the theoretical material covered in more traditional lectures and homeworks. Courses at other institutions have created labs with a similar goal in mind. However, many have a hardware component or involve in-person lab sections that require teaching staff to monitor progress. This presents a significant barrier for deployment in larger courses. Virtual labs—in particular, pure software assignments using the Jupyter Notebook framework—recently emerged as a solution to this problem. Some courses use programming-only labs that lack the modularity and rich user interface of Jupyter Notebook’s cell-based design. Other labs based on the Jupyter Notebook have not yet tapped the full potential of its versatile features. Our labs (1) demonstrate real-life applications; (2) cultivate computational literacy; and (3) are structured to be self-contained. These design principles reduce overhead for teaching staff and give students relevant experience for research and industry.Carrano, D.; Chugunov, I.; Lee, J.; Ayazifar, B. (2020). Self-Contained Jupyter Notebook Labs Promote Scalable Signal Processing Education. En 6th International Conference on Higher Education Advances (HEAd'20). Editorial Universitat Politècnica de València. (30-05-2020):1409-1416. https://doi.org/10.4995/HEAd20.2020.11308OCS1409141630-05-202

Advanced Television Research Program

Contains an introduction and reports on twelve research projects.Advanced Television Research ProgramNational Science Foundation Grant MIP 87-14969National Science Foundation FellowshipKodak Fellowshi

Advanced Television and Signal Processing Program

Contains an introduction and reports on fifteen research projects.Advanced Television Research ProgramAdams-Russell Electronics, Inc.National Science Foundation Fellowship Grant MIP 87-14969National Science Foundation FellowshipU.S. Navy - Office of Naval Research Grant N00014-89-J-1489U.S. Air Force - Electronic Systems Division Contract F1 9628-89-K-004

Pel-adaptive model-based interpolation of spatially subsampled images

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1992.Includes bibliographical references (leaves 53-55).by Babak Ayazifar.M.S

Critically-sampled perfect-reconstruction spline-wavelet filterbanks for graph signals

Inspired by first-order spline wavelets in classical signal processing, we introduce two-channel (low-pass and high-pass), critically-sampled, perfect-reconstruction filterbanks for signals defined on circulant graphs, which accommodate linear shift-invariant filtering. We then generalize to filters that process signals defined on noncirculant graphs. We apply these filters, which can be tuned to approximate desired frequency responses, to synthetic graphs and examine their performance

FOURIER ANALYSIS OF AUDIO SIGNALS 7

In this lab session, we will use the theory of, and the concepts behind, the Discrete-Time Fourier Series (DTFS or DFS) in different applications involving audio signals. In the in-lab sections, we will separate the voices of the different frog species present in a given sound sample; in a related exercise, we will also alter the frequency of a voice sample. Along the way, we will study and determine how altering the frequenc

Multiresolution graph signal processing via circulant structures

We offer a new paradigm for multiresolution analysis and process-ing of graph signals using circulant structures. Among the essential features of circulant graphs is that they accommodate fundamental signal processing operations, such as linear shift-invariant filtering, downsampling, upsampling, and reconstruction—features that we take to substantial advantage. We design two-channel, critically-sampled, perfect-reconstruction, orthogonal lattice-filter structures to process signals on circulant graphs. To extend our reach to more general graphs, we present a method to decompose a connected, undirected graph into a linear combination of circulant graphs. Our circulant decomposition is analogous to designing linear time-varying lattice filters by suitably adapting the coefficients of a linear time-invariant filter. To evaluate the systems and methods that we have propounded, we offer examples of synthetic and real-world graph datasets and their multiscale decompositions