The two volumes of Signal Processing are based on lectures delivered during a six week program held at the IMA from June 27 to August 5, 1988. The first two weeks of the program dealt with general areas and methods of Signal Pro­ cessing. The problem areas included imaging and analysis of recognition, x-ray crystallography, radar and sonar, signal analysis and 1-D signal processing, speech, vision, and VLSI implementation. The methods discussed included harmonic anal­ ysis and wavelets, operator theory, algorithm complexity, filtering and estimation, and inverse scattering. The topics of weeks three and four were digital filter, VLSI implementation, and integrable circuit modelling. In week five the concentration was on robust and nonlinear control with aerospace applications, and in week six the emphasis was on problems in radar, sonar and medical imaging. Because of the large overlap between the various one-week and two-week seg­ ments of the program, we found it more convenient to divide the material somewhat differently. Part I deals with general signal process theory and Part II deals with (i) application of signal processing, (ii) control theory related themes. We are grateful to the scientific organizers: Tom Kailath (Chairman), Louis Aus­ lander, F. Alberto Grunbaum, J. William Helton, Pramod P. Khargonekar and Sanjoy K. Mitter. We are also grateful for the generous support given to the IMA program by the Office of Naval Research, the Air Force Office of Scientific Research, the Army Research Office and the National Security Agency.

I - Control Theory.- Sensitivity minimization and bitangential Nevanlinna-pick interpolation in contour integral form.- Uniform bounded input-bounded output stabilization of nonlinear systems.- Operator theoretic methods in the control of distributed and nonlinear systems.- Snippets of ?? control theory.- Nongaussian linear filtering, identification of linear systems, and the symplectic group.- Approximation of Hankel operators: truncation error in an H? design method.- Nonlinear controller design via approximate normal forms.- Feedback with delays: Stabilization of linear time-delay and two-dimensional systems.- Control structure selection: Issues and a new methodology.- II - Applications of Signal Processing.- Tomography in radar.- Local and global tomography.- The phase problem of X-Ray crystallography.- Inversion of the X-ray transform from data in a limited angular range.- The eikonal approximation in ultrasound computer tomography.- Radar signal choice and processing for a dense target environment.- Basic algorithms in tomography.- High resolution radar imaging using spectrum estimation methods.- Limited data tomography in non-destructive evaluation.- Speech recognition based on pattern recognition approaches.- ESPRIT - estimation of signal parameters via rotational invariance techniques.