  An exact solution of the homogeneous wave equation, which was found
previously, is treated from the point of view of continuous wavelet analysis
(CWA). If time is a fixed parameter, the solution represents a new
multidimensional mother wavelet for the CWA. Both the wavelet and its Fourier
transform are given by explicit formulas and are exponentially localized. The
wavelet is directional. The widths of the wavelet and the uncertainty relation
are investigated numerically. If a certain parameter is large, the wavelet
behaves asymptotically as the Morlet wavelet. The solution is a new physical
wavelet in the definition of Kaiser, it may be interpreted as a sum of two
parts: an advanced and a retarded part, both being fields of a pulsed point
source moving at a speed of wave propagation along a straight line in complex
space-time.
