**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**

**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**