Triple Product Processor

A variety of acoustooptic signal processing architectures capable of producing triple products in real time are reviewed. As well a status report on the construction of a high bandwidth interf erometric triple product processor is given. where T is an interval. Using this generic integral and suitable choices of the functions f(t), g(t), and h(t), a variety of signal processing operations can be formed l~3 . An example of such a process is the ambiguity function ** : X(T,$)=/~QO u(t)u*(t+T)exp(-i$t)dt (2) where u(t) is an input function and u* (t) is its complex conjugate. The correspondence between equations 1 and 2 is established via the following definitions: f (t)=u(t)exp(-i(o)+Bt) t) (3) g(t)=u*(t) (4) h(t)=exp(i(w+3t) t) (5) where w is the starting frequency of the chirp and 3 is its rate of increase in frequency. These substitutions produce ah ambiguity function which is multiplied by a quadratic phase term, this term is unimportant when using intensity detectors. The function g(t) could also be made a chirp and to multiply the input function u(t), resulting in a raster transform 5 . The spectrum formed by the raster transform can have a very large time bandwidth product ^ 10 6. Lohmann6 gives an excellent discussion of some other uses of the triple product, such as signal extraction from noise. In this paper some acoustooptic signal processor architectures capable of producing triple products in real time, are reviewed. The bandwidth, stability, and optical efficiency of these architectures is discussed, as well as the degree of completeness of the triple product obtained from them. Also a status report on the construction of a high bandwidth triple product processor is given.