Synopses of Research Foci (under construction!)

 

 

Topic:                               Multiple-channel detection

Main Collaborators:       Herb Gish, Dana Sinno, Axel Clausen, Louis Scharf, Stephen Howard, Songsri Sirianunpiboon

 

In 1989, Herb Gish and I introduced the Generalized Coherence (GC) Estimate [1-1] as a statistic to test for correlation among multiple complex vectors and derived its null distribution.  In 1995, together with Dana Sinno, we elaborated on the geometrical nature of this statistic and on its merits as a statistic for multi-channel detection of an unknown signal [1-2]. 

 

 

Topic:                               Sampling of time-warped signals

Main Collaborators:       Jim Clark, John Mc Donald, Shahrnaz Azizi

 

One element of my Ph.D. thesis, this part supervised by Jim Clark, examined the class of signals h on the real line that are formed by composition of a bandlimited signal f with an invertible “warping” function g; i.e., h(t)=f(g(t)). In the early 1990s, Jim and I published several results pertaining to sampling, reconstruction, and representational uniqueness for such signals; e,g, [2-1], [2-2]. In the late 1990s, joint work with John Mc Donald and Shahrnaz Azizi [2-3], [2-4] used this perspective to satisfactorily sort out the “folk theorem” that h will be bandlimited if and only if g is affine.  The essence of the answer is that a particular h, formed from a particular f and g, might be bandlimited even if g is not affine.  But if g yields a bandlimited function for every h, then g must be affine.

 

 

Topic:                               Design of waveforms and waveform libraries

Main Collaborators:       Bill Moran, Sofia Suvorova, Stephen Howard, Sandeep Sira, Rob Calderbank

 

 

Topic:                               Detection of cyclostationary signals

Main Collaborators:       Scott Enserink

 

[3-1], [3-2]

 

 

Topic:                               Design of waveforms and waveform libraries

Main Collaborators:       Bill Moran, Sofia Suvorova, Stephen Howard, Sandeep Sira, Rob Calderbank

 

 

 

Topic:                               Bounds related to frames

Main collaborators:        Somantika Datta, Stephen Howard