Alan Oppenheim (Massachusetts Institute of Technology)
Digital processing of analog signals naturally requires a
representation of continuous time signals as a discrete-time
sequence. The most common representation of this type is based on
the Shannon-Nyquist sampling theorem which provides an exact
representation for band limited signals sampled at a sufficiently
high rate but leads to aliasing error when the signal is under
sampled. In this talk a number of other approaches are discussed
to obtaining discrete-time representations that avoid or mitigate
the effects of aliasing. These include other basis expansions such
as bilinear sampling and wavelets, and modified sampling
strategies such as non-uniform sampling and randomized sampling.
The use of randomization in filter and array implementation and
its relation to randomized sampling will also be discussed.