Sampling Signals with Finite Rate of Innovation
Tuesday, Sep. 17, 2002
2:00-3:30 p.m.
Hughes Room
Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. Call the number of degrees of freedom per unit of time the rate of innovation. We demonstrate that by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation, one can uniquely reconstruct such signals.

We thus prove theorems for classes of signals and sampling kernels that generalize the classic ``bandlimited and sinc kernel'' case. In particular, we show sampling theorems for periodic as well as finite length piecewise polynomials, using a bandlimited derivative kernel, as well as a Gaussian kernel. For infinite length piecewise polynomials with a finite local rate of innovation, we show exact local reconstruction using sampling with spline kernels. We also show some extensions to the sampling of the Radon transform, as well as methods for dealing with the noisy case.

All the results presented lead to computational procedures that are readily implementable, which is shown through experimental results. Applications of these new sampling results can be found in signal processing, communications systems and biological systems.

In particular, we will show how these results can be used for ultra-wideband (UWB) communication systems, as well as in CDMA, reducing sampling rates for receivers by potentially an order of magnitude.

This is joint work with T.Blu, I.Maravic and P.Marziliano

UC Berkeley Networking
Ashwin Pananjady and Orhan Ocal
Last Modification Date: Wednesday, February 10, 2016