Space-time-scale analysis of electromagnetic waves

The previously defined analytic-signal transform is used to extend electromagnetic waves from real space-time to complex space-time. This leads naturally to a family of elementary conformal wavelets, which can all be obtained by applying conformal transformations of space-time to a basic wavelet. The basic wavelet, is uniquely determined by analyticity considerations. These wavelets are parametrized by location x, time t, scale s and velocity v. An arbitrary wave can be decomposed into either stationary or moving wavelets. Such decompositions may be useful in the analysis of waves emitted by a moving source. There also exist decompositions suitable for accelerating sources