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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 five 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.