The Digital Signal Processing Group in the MIT Research Laboratory of Electronics focuses on developing general methods for signal processing that can be applied to a wide range of applications.  Our research over the last four decades has focused both on traditional areas such as signal modeling, sampling and signal representations, and signal estimation, and on unconventional topics such as fractal signals, chaotic behavior in nonlinear dynamic systems, and solitary waves generated by certain nonlinear wave equations.  Some of the specific classes of signals that we have studied include speech, images sensor network data, communication signals, and signals associated with problems in ocean acoustics.   We also often look to nature for inspiration and as a metaphor for new signal processing directions, such as our recent work titled Quantum Signal Processing, which was inspired by quantum mechanics.

Our current work encompasses a broad set of aims including the exploration of new areas of mathematics, the development of new algorithms for distributed signal processing, a variety of new sampling and interpolation methods, new approaches to nonlinear signal processing, and various issues at the interface of signal processing and biology.

One recent set of projects concerns various approaches to the reconstruction of signals from uniform and nonuniform samples.  Among other applications, our results have been applied to digital pre-compensation for faulty D/A converters.  In some contexts, DACs fail in such a way that specific samples are dropped.  For example, in flat-panel video displays one of the pixel LEDs can malfunction and become permanently set to a particular value.  We refer to this as the "missing pixel'' problem.  Our results on reconstruction from nonuniform samples have been used to compensate for the dropped sample by pre-processing the digital signal.  We continue to explore a number of such compensation strategies.   Of particular interest is the relationship between compensation and the class of discrete prolate spheroidal sequences.  Also related to sampling and reconstruction is our work on exploring new digital filter configurations for efficient upsampling and interpolation and in particular the combined use of FIR and IIR structures.

In the general area of signal processing algorithms, we have been investigating several areas of mathematics such as geometric algebras and frame theory with the goal of developing new classes of algorithms with broad application.  We are also currently exploring various classes of nonlinear signal processing.  Some are based on viewing nonlinearities as linear in higher dimensional spaces.  Others are based on exploiting nonlinear superposition.   In this category we are studying new aspects of cepstral analysis and also exploring other homomorphic systems and applications to the method of generalized superposition.  We are particularly interested in searching for subclasses of non-linear systems with properties that may be exploited to allow the systems to be considered linear or to offer insight into the non-linearities of these systems.

Distributed signal processing represents another important area of our research.  An important trend in signal processing technology is the increasing deployment of distributed signal processing systems; i.e., systems in which signal measurement, storage and processing capacity are separated by a communication network.  Examples range from board-level multiprocessor systems to systems-on-a-chip, to wireless sensor networks.  In many cases, the communication network can form the critical bottleneck on important performance parameters such as processing speed or power consumption.  There are a wide variety of techniques to deal with the communication network in a distributed system.  We are investigating data selection, a lossy compression technique, as a way to reduce the communication cost of distributed signal processing.  Our algorithms select a subset of the data that can be communicated easily through the network, yet yield accurate results when used as input to various signal processing algorithms.  We have focused on the design of signal detection algorithms in a variety of contexts, including the detection of known signals with a matched filter and robust detection of signals in Gaussian noise.

Biological Signal Processing and–in particular–issues and opportunities at the interface of biology and signal processing represent another important research thrust in DSPG.  Our research focuses on introducing systematic engineering principles to model, at different levels of abstractions, the information processing in biological cells in order to understand the algorithms implemented by the signaling pathways that perform the processing.  We are also investigating ways to emulate these algorithms in other contexts such as engineered distributed networks.  The goal is to develop mathematical models for biological signal processing at the protein and DNA level at different levels of abstraction.   At the highest level, the dynamical properties of the components of the signaling network are ignored and the focus is on the network topology.  In this regime, the distribution and properties of the network graph are examined and analyzed.  At the lowest level, the thesis introduces a new framework for modeling cellular signal processing based on interacting Markov chains.  The question of how the topologies and dynamics of biological signaling networks confer given system properties and characteristics is being investigated and analyzed within biological experimental data.  Furthermore, the evolution of these networks to accommodate new properties and responses is being examined.  The research also exploits the models introduced and our understanding of how cells perform signal processing in engineered networks.  We anticipate that this work will lead to new algorithms for signal processing on distributed networks.